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  • 1.
    Abramowicz, Konrad
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Numerical analysis for random processes and fields and related design problems2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, we study numerical analysis for random processes and fields. We investigate the behavior of the approximation accuracy for specific linear methods based on a finite number of observations. Furthermore, we propose techniques for optimizing performance of the methods for particular classes of random functions. The thesis consists of an introductory survey of the subject and related theory and four papers (A-D).

    In paper A, we study a Hermite spline approximation of quadratic mean continuous and differentiable random processes with an isolated point singularity. We consider a piecewise polynomial approximation combining two different Hermite interpolation splines for the interval adjacent to the singularity point and for the remaining part. For locally stationary random processes, sequences of sampling designs eliminating asymptotically the effect of the singularity are constructed.

    In Paper B, we focus on approximation of quadratic mean continuous real-valued random fields by a multivariate piecewise linear interpolator based on a finite number of observations placed on a hyperrectangular grid. We extend the concept of local stationarity to random fields and for the fields from this class, we provide an exact asymptotics for the approximation accuracy. Some asymptotic optimization results are also provided.

    In Paper C, we investigate numerical approximation of integrals (quadrature) of random functions over the unit hypercube. We study the asymptotics of a stratified Monte Carlo quadrature based on a finite number of randomly chosen observations in strata generated by a hyperrectangular grid. For the locally stationary random fields (introduced in Paper B), we derive exact asymptotic results together with some optimization methods. Moreover, for a certain class of random functions with an isolated singularity, we construct a sequence of designs eliminating the effect of the singularity.

    In Paper D, we consider a Monte Carlo pricing method for arithmetic Asian options. An estimator is constructed using a piecewise constant approximation of an underlying asset price process. For a wide class of Lévy market models, we provide upper bounds for the discretization error and the variance of the estimator. We construct an algorithm for accurate simulations with controlled discretization and Monte Carlo errors, andobtain the estimates of the option price with a predetermined accuracy at a given confidence level. Additionally, for the Black-Scholes model, we optimize the performance of the estimator by using a suitable variance reduction technique.

  • 2.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Arnqvist, Per
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sjöstedt de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Secchi, Piercesare
    Vantini, Simone
    Vitelli, Valeria
    Was it snowing on lake Kassjön in January 4486 BC? Functional data analysis of sediment data.2014In: Proceedings of the Third International Workshop on Functional and Operatorial Statistics (IWFOS 2014), Stresa, Italy, June 2014., 2014Conference paper (Refereed)
  • 3.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Häger, Charlotte
    Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Hérbert-Losier, Kim
    National Sports Institute of Malaysia.
    Pini, Alessia
    MOX – Department of Mathematics, Politecnico di Milano.
    Schelin, Lina
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics. Umeå University, Faculty of Medicine, Department of Community Medicine and Rehabilitation, Physiotherapy.
    Strandberg, Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Vantini, Simone
    MOX – Department of Mathematics, Politecnico di Milano.
    An inferential framework for domain selection in functional anova2014In: Contributions in infinite-dimensional statistics and related topics / [ed] Bongiorno, E.G., Salinelli, E., Goia, A., Vieu, P, Esculapio , 2014Conference paper (Refereed)
    Abstract [en]

    We present a procedure for performing an ANOVA test on functional data, including pairwise group comparisons. in a Scheff´e-like perspective. The test is based on the Interval Testing Procedure, and it selects intervals where the groups significantly differ. The procedure is applied on the 3D kinematic motion of the knee joint collected during a functional task (one leg hop) performed by three groups of individuals.

  • 4.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Seleznjev, Oleg
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On the error of the Monte Carlo pricing method for Asian option2008In: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 96, no 1, p. 1-10Article in journal (Refereed)
    Abstract [en]

    We consider a Monte Carlo method to price a continuous arithmetic Asian option with a given precision. Piecewise constant approximation and plain simulation are used for a wide class of models based on L\'{e}vy processes. We give bounds of the possible discretization and simulation errors. The sufficient numbers of discretization points and simulations to obtain requested accuracy are derived. To demonstrate the general approach, the Black-Scholes model is studied in more detail. We undertake the case of continuous averaging and starting time zero,  but the obtained results can be applied to the discrete case  and generalized for any time before an execution date. Some numerical experiments and comparison to the PDE based method are also presented.

  • 5.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Seleznjev, Oleg
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Piecewise multilinear interpolation of a random field2013In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 45, no 4, p. 945-959Article in journal (Refereed)
    Abstract [en]

    We consider a piecewise-multilinear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured using the integrated mean square error. Piecewise-multilinear interpolator is defined by N-field observations on a locations grid (or design). We investigate the class of locally stationary random fields whose local behavior is like a fractional Brownian field, in the mean square sense, and find the asymptotic approximation accuracy for a sequence of designs for large N. Moreover, for certain classes of continuous and continuously differentiable fields, we provide the upper bound for the approximation accuracy in the uniform mean square norm.

  • 6.
    Abramowicz, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Seleznjev, Oleg
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Stratified Monte Carlo quadrature for continuous random fields2015In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 17, no 1, p. 59-72Article in journal (Refereed)
    Abstract [en]

    We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is defined by a finite number of stratified randomly chosen observations with the partition generated by a rectangular grid (or design). We study the class of locally stationary random fields whose local behavior is like a fractional Brownian field in the mean square sense and find the asymptotic approximation accuracy for a sequence of designs for large number of the observations. For the H¨older class of random functions, we provide an upper bound for the approximation error. Additionally, for a certain class of isotropic random functions with an isolated singularity at the origin, we construct a sequence of designs eliminating the effect of the singularity point.

  • 7.
    Abramowizc, Konrad
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Arnqvist, Per
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Secchi, Piercesare
    Politecnico di Milano, Italy.
    Sjöstedt de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Vantini, Simone
    Politecnico di Milano, Italy.
    Vitelli, Valeria
    Oslo University, Norway.
    Clustering misaligned dependent curves applied to varved lake sediment for climate reconstruction2017In: Stochastic environmental research and risk assessment (Print), ISSN 1436-3240, E-ISSN 1436-3259, Vol. 31, no 1, p. 71-85Article in journal (Refereed)
    Abstract [en]

    In this paper we introduce a novel functional clustering method, the Bagging Voronoi K-Medoid Aligment (BVKMA) algorithm, which simultaneously clusters and aligns spatially dependent curves. It is a nonparametric statistical method that does not rely on distributional or dependency structure assumptions. The method is motivated by and applied to varved (annually laminated) sediment data from lake Kassjön in northern Sweden, aiming to infer on past environmental and climate changes. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.

  • 8.
    Abramsson, Evelina
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Grind, Kajsa
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Skattning av kausala effekter med matchat fall-kontroll data2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 9.
    Alainentalo, Lisbeth
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A Comparison of Tests for Ordered Alternatives With Application in Medicine1997Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    A situation frequently encountered in medical studies is the comparison of several treatments with a control. The problem is to determine whether or not a test drug has a desirable medical effect and/or to identify the minimum effective dose. In this Bachelor’s thesis, some of the methods used for testing hypotheses of ordered alternatives are reviewed and compared with respect to the power of the tests. Examples of multiple comparison procedures, maximum likelihood procedures, rank tests and different types of contrasts are presented and the properties of the methods are explored.

    Depending on the degree of knowledge about the dose-responses, the aim of the study, whether the test is parametric or non-parametric and distribution-free or not, different recommendations are given which of the tests should be used. Thus, there is no single test which can be applied in all experimental situations for testing all different alternative hypotheses. 

  • 10.
    Albing, Malin
    et al.
    Department of Mathematics, Luleå University of Technology.
    Vännman, Kerstin
    Department of Mathematics, Luleå University of Technology.
    Elliptical safety region plots for Cpk2011In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 38, no 6, p. 1169-1187Article in journal (Refereed)
    Abstract [en]

    The process capability index C pk is widely used when measuring the capability of a manufacturing process. A process is defined to be capable if the capability index exceeds a stated threshold value, e.g. C pk >4/3. This inequality can be expressed graphically using a process capability plot, which is a plot in the plane defined by the process mean and the process standard deviation, showing the region for a capable process. In the process capability plot, a safety region can be plotted to obtain a simple graphical decision rule to assess process capability at a given significance level. We consider safety regions to be used for the index C pk . Under the assumption of normality, we derive elliptical safety regions so that, using a random sample, conclusions about the process capability can be drawn at a given significance level. This simple graphical tool is helpful when trying to understand whether it is the variability, the deviation from target, or both that need to be reduced to improve the capability. Furthermore, using safety regions, several characteristics with different specification limits and different sample sizes can be monitored in the same plot. The proposed graphical decision rule is also investigated with respect to power.

  • 11.
    Alger, Susanne
    Umeå University, Faculty of Social Sciences, Department of applied educational science.
    Is This Reliable Enough?: Examining Classification Consistency and Accuracy in a Criterion-Referenced Test2016In: International journal of assessment tools in education, ISSN 2148-7456, Vol. 3, no 2, p. 137-150Article in journal (Refereed)
    Abstract [en]

    One important step for assessing the quality of a test is to examine the reliability of test score interpretation. Which aspect of reliability is the most relevant depends on what type of test it is and how the scores are to be used. For criterion-referenced tests, and in particular certification tests, where students are classified into performance categories, primary focus need not be on the size of error but on the impact of this error on classification. This impact can be described in terms of classification consistency and classification accuracy. In this article selected methods from classical test theory for estimating classification consistency and classification accuracy were applied to the theory part of the Swedish driving licence test, a high-stakes criterion-referenced test which is rarely studied in terms of reliability of classification. The results for this particular test indicated a level of classification consistency that falls slightly short of the recommended level which is why lengthening the test should be considered. More evidence should also be gathered as to whether the placement of the cut-off score is appropriate since this has implications for the validity of classifications.

  • 12.
    Andersdotter Persson, Anna
    Umeå University, Faculty of Social Sciences, Department of Statistics.
    Kalibrering som ett sätt att hantera bortfall: Vilken korrelation krävs mellan hjälp- och responsvariabler?2010Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
  • 13.
    Andersson, Björn
    Umeå University, Faculty of Social Sciences, Department of Statistics.
    Consequences of near-unfaithfulness in a finite sample: a simulation study2010Independent thesis Advanced level (degree of Master (Two Years)), 10 credits / 15 HE creditsStudent thesis
  • 14.
    Andersson, Björn
    et al.
    Uppsala universitet.
    Bränberg, Kenny
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Wiberg, Marie
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    kequate: The kernel method of test equating. R package version 1.1.02012Other (Other academic)
    Abstract [en]

    Implements the kernel method of test equating using the CB, EG, SG, NEAT CE/PSE and NEC designs, supporting gaussian,logistic and uniform kernels and unsmoothed and pre-smoothed input data.

  • 15.
    Andersson, Björn
    et al.
    Uppsala universitet.
    Bränberg, Kenny
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Wiberg, Marie
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Performing the Kernel Method of Test Equating with the Package kequate2013In: Journal of Statistical Software, ISSN 1548-7660, E-ISSN 1548-7660, Vol. 55, no 6, p. 1-25Article in journal (Refereed)
    Abstract [en]

    In standardized testing it is important to equate tests in order to ensure that the test takers, regardless of the test version given, obtain a fair test. Recently, the kernel method of test equating, which is a conjoint framework of test equating, has gained popularity. The kernel method of test equating includes five steps: (1) pre-smoothing, (2) estimation of the score probabilities, (3) continuization, (4) equating, and (5) computing the standard error of equating and the standard error of equating difference. Here, an implementation has been made for six different equating designs: equivalent groups, single group, counter balanced, non-equivalent groups with anchor test using either chain equating or post- stratification equating, and non-equivalent groups using covariates. An R package for the kernel method of test equating called kequate is presented. Included in the package are also diagnostic tools aiding in the search for a proper log-linear model in the pre-smoothing step for use in conjunction with the R function glm.

  • 16.
    Andersson, Björn
    et al.
    Statistiska institutionen, Uppsala universitet.
    Waernbaum, Ingeborg
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Sensitivity analysis of violations of the faithfulness assumption2014In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 84, no 7, p. 1608-1620Article in journal (Other academic)
    Abstract [en]

    We study implications of violations of the fatihfulness condition due to parameter cancellations on estimation of the DAG skeleton. Three settings are investigated: when i) faithfulness is guaranteed ii) faithfulness is not guaranteed and iii) the parameter distributions are concentrated around unfaithfulness (near-unfaithfulness). In a simulation study the effetcs of the different settings are compared using the PC and MMPC algorithms. The results show that the performance in the faithful case is almost unchanged compared to the unrestricted case whereas there is a general decrease in performance under the near-unfaithful case as compared to the unrestricted case. The response to near-unfaithful parameterisations is similar between two algorithms, with the MMPC algorithm having higher true positive rates and the PC algorithm having lower false positive rates.

  • 17.
    Andersson, Björn
    et al.
    Beijing Normal University.
    Wiberg, Marie
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Item response theory observed-score kernel equating2017In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 82, no 1, p. 48-66Article in journal (Refereed)
    Abstract [en]

    Item response theory (IRT) observed-score kernel equating is introduced for the non-equivalent groups with anchor test equating design using either chain equating or post-stratification equating. The equating function is treated in a multivariate setting and the asymptotic covariance matrices of IRT observed-score kernel equating functions are derived. Equating is conducted using the two-parameter and three-parameter logistic models with simulated data and data from a standardized achievement test. The results show that IRT observed-score kernel equating offers small standard errors and low equating bias under most settings considered.

  • 18.
    Andersson, Niklas
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Regression-Based Monte Carlo For Pricing High-Dimensional American-Style Options2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Pricing different financial derivatives is an essential part of the financial industry. For some derivatives there exists a closed form solution, however the pricing of high-dimensional American-style derivatives is still today a challenging problem. This project focuses on the derivative called option and especially pricing of American-style basket options, i.e. options with both an early exercise feature and multiple underlying assets. In high-dimensional problems, which is definitely the case for American-style options, Monte Carlo methods is advantageous. Therefore, in this thesis, regression-based Monte Carlo has been used to determine early exercise strategies for the option. The well known Least Squares Monte Carlo (LSM) algorithm of Longstaff and Schwartz (2001) has been implemented and compared to Robust Regression Monte Carlo (RRM) by C.Jonen (2011). The difference between these methods is that robust regression is used instead of least square regression to calculate continuation values of American style options. Since robust regression is more stable against outliers the result using this approach is claimed by C.Jonen to give better estimations of the option price.

    It was hard to compare the techniques without the duality approach of Andersen and Broadie (2004) therefore this method was added. The numerical tests then indicate that the exercise strategy determined using RRM produces a higher lower bound and a tighter upper bound compared to LSM. The difference between upper and lower bound could be up to 4 times smaller using RRM.

    Importance sampling and Quasi Monte Carlo have also been used to reduce the variance in the estimation of the option price and to speed up the convergence rate.

  • 19.
    Andersson Tano, Ingrid
    et al.
    Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden.
    Vännman, Kerstin
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    A multivariate process capability index based on the first principal component only2013In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 29, no 7, p. 987-1003Article in journal (Refereed)
    Abstract [en]

    Often the quality of a process is determined by several correlated univariate variables. In such cases, the considered quality characteristic should be treated as a vector. Several different multivariate process capability indices (MPCIs) have been developed for such a situation, but confidence intervals or tests have been derived for only a handful of these. In practice, the conclusion about process capability needs to be drawn from a random sample, making confidence intervals or tests for the MPCIs important. Principal component analysis (PCA) is a well-known tool to use in multivariate situations. We present, under the assumption of multivariate normality, a new MPCI by applying PCA to a set of suitably transformed variables. We also propose a decision procedure, based on a test of this new index, to be used to decide whether a process can be claimed capable or not at a stated significance level. This new MPCI and its accompanying decision procedure avoid drawbacks found for previously published MPCIs with confidence intervals. By transforming the original variables, we need to consider the first principal component only. Hence, a multivariate situation can be converted into a familiar univariate process capability index. Furthermore, the proposed new MPCI has the property that if the index exceeds a given threshold value the probability of non-conformance is bounded by a known value. Properties, like significance level and power, of the proposed decision procedure is evaluated through a simulation study in the two-dimensional case. A comparative simulation study between our new MPCI and an MPCI previously suggested in the literature is also performed. These studies show that our proposed MPCI with accompanying decision procedure has desirable properties and is worth to study further.

  • 20.
    Andersson Tano, Ingrid
    et al.
    Department of Engineering Sciences and Mathematics, Luleå University of Technology, Luleå, Sweden.
    Vännman, Kerstin
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Comparing confidence intervals for multivariate process capability indices2012In: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 28, no 4, p. 481-495Article in journal (Refereed)
    Abstract [en]

    Multivariate process capability indices (MPCIs) are needed for process capability analysis when the quality of a process is determined by several univariate quality characteristics that are correlated. There are several different MPCIs described in the literature, but confidence intervals have been derived for only a handful of these. In practice, the conclusion about process capability must be drawn from a random sample. Hence, confidence intervals or tests for MPCIs are important. With a case study as a start and under the assumption of multivariate normality, we review and compare four different available methods for calculating confidence intervals of MPCIs that generalize the univariate index Cp. Two of the methods are based on the ratio of a tolerance region to a process region, and two are based on the principal component analysis. For two of the methods, we derive approximate confidence intervals, which are easy to calculate and can be used for moderate sample sizes. We discuss issues that need to be solved before the studied methods can be applied more generally in practice. For instance, three of the methods have approximate confidence levels only, but no investigation has been carried out on how good these approximations are. Furthermore, we highlight the problem with the correspondence between the index value and the probability of nonconformance. We also elucidate a major drawback with the existing MPCIs on the basis of the principal component analysis. Our investigation shows the need for more research to obtain an MPCI with confidence interval such that conclusions about the process capability can be drawn at a known confidence level and that a stated value of the MPCI limits the probability of nonconformance in a known way.

  • 21.
    Andersson, Tobias
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Golovlev, Jegor
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Prediktion av bruttoregionalprodukt: Prognosmodellering som förkortar tiden mellan officiella siffror och prognos2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Arbetet har utforskat möjligheten och precisionen av BRP-prediktion för tre statistiska metoder; linjär regression, regressionsträd och modellträd. För modellutvärdering har testfelsskattning erhållen genom korsvalidering och en jämförelse mot Statistiska Centralbyråns (SCB) prognos av BRP används. Resultatet visar att regressionsträd inte lämpar sig för BRP-prediktion, medan de andra två lyckas med rimlig felmarginal. Procentuell avvikelse för metoden som ligger närmast SCB:s prognos har 0,3 i genomsnitt och standardavvikelse 3,0.

  • 22.
    Angelov, Angel G.
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Ekström, Magnus
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Nonparametric estimation for self-selected interval data collected through a two-stage approach2017In: Metrika (Heidelberg), ISSN 0026-1335, E-ISSN 1435-926X, Vol. 80, no 4, p. 377-399Article in journal (Refereed)
    Abstract [en]

    Self-selected interval data arise in questionnaire surveys when respondents are free to answer with any interval without having pre-specified ranges. This type of data is a special case of interval-censored data in which the assumption of noninformative censoring is violated, and thus the standard methods for interval-censored data (e.g. Turnbull's estimator) are not appropriate because they can produce biased results. Based on a certain sampling scheme, this paper suggests a nonparametric maximum likelihood estimator of the underlying distribution function. The consistency of the estimator is proven under general assumptions, and an iterative procedure for finding the estimate is proposed. The performance of the method is investigated in a simulation study.

  • 23.
    Anton, Rikard
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Cohen, David
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Univ Innsbruck, Dept Math, Innsbruck, Austria.
    Larsson, Stig
    Wang, Xiaojie
    Full discretization of semilinear stochastic wave equations driven by multiplicative noise2016In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 54, no 2, p. 1093-1119Article in journal (Refereed)
    Abstract [en]

    A fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space, and a stochastic trigonometric method is used for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretization and thus does not suffer from a step size restriction as in the often used Stormer-Verlet leapfrog scheme. Furthermore, it satisfies an almost trace formula (i.e., a linear drift of the expected value of the energy of the problem). Numerical experiments are presented and confirm the theoretical results.

  • 24.
    Arnqvist, Per
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Allowing Left Truncated and Censored Fertility Data in the Normal Waiting Model1995Report (Other academic)
    Abstract [en]

    Models describing marital fertility are under consideration. In Arnqvist (Research Report 2, Mathematical Statistics, Umeå University), a normal approximation of the waiting model was introduced. In this report a modification of the normal approximation is suggested. This specification allows the data to be left truncated and censored, which gives the possibility to apply the normally approximated waiting model in datasets as from the United Nations World Fertility Services. The model is appropriate except for extremely high fertility intensities, when it gives rise to bias in the parameter estimations. In this case, therefore, a bootstrap method is suggested to estimate and correct the bias. This means that the normal approximated waiting model is a good competitor to the well known Poisson or Coale-Trussell model. It also uses an understandable fertility specification.

  • 25.
    Arnqvist, Per
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Approximation of the waiting model1995Report (Other academic)
    Abstract [en]

    In an attempt to estimate the level of family planning in a population, Coale-Trussell suggested an intensity model based on five year summarized data as given in the reports of the United Nations. Their model is denoted Coale-Trussell model. To make inference in the model, it was assumed that the pregnancy data in the model followed a Poisson process. In Arnqvist (research report 1, 1995, Mathematical Statistics, Umeå University), a modification of the Poisson assumption in the intensity model was suggested, introducing waiting time after the pregnancies. The resulting model was named the waiting model. The aim of this paper is to compare the Coale-Trussell model with the waiting model when data of the form given in UN World Fertility Surveys are used (Table 1). By using a normal approximation of the first two moments of the number of pregnancies, the asymptotic variance of the estimators of the interesting parameters is given. Simulation studies show that the Coale-Trussell model and the normal approximation model both approximate the lower intensities in the waiting model well. However, the Coale-Trussell model gives essentially biased estimates of the intensities for high birth intensities.

  • 26.
    Arnqvist, Per
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Aspects of the Coale-Trussell Model1995Report (Other academic)
    Abstract [en]

    Coale-Trussell model for marital fertility is investigated. The assumption that the data follow a Poisson model is invalidated by empirical evidence. The data are less spread than assumed, which indicates a point process which is undersdispersed relative to the Poisson model. By generalizing the Poisson model, by using a more realistic assumption about spacing between births, eg. allowing for a constant delay after each birth, we produce a better and more natural descripton of human reproduction.

  • 27.
    Arnqvist, Per
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Functional clustering methods and marital fertility modelling2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population.

    The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions.

    A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent curves. BVKMA is used on the varved lake sediment, to infer on climate, defined as frequencies of different weather types, over longer time periods.

    Furthermore, a functional model-based clustering method is proposed that clusters subjects for which both functional data and covariates are observed, allowing different covariance structures in the different clusters. The model extends a model-based functional clustering method proposed by James and Suger (2003). An EM algorithm is derived to estimate the parameters of the model.

  • 28.
    Arnqvist, Per
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Bigler, Christian
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Renberg, Ingemar
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Sjöstedt de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Functional clustering of varved lake sediment to reconstruct past seasonal climate2016In: Environmental and Ecological Statistics, ISSN 1352-8505, E-ISSN 1573-3009, Vol. 23, no 4, p. 513-529Article in journal (Refereed)
    Abstract [en]

    Annually laminated (varved) lake sediments constitutes excellent environmental archives, and have the potential to play an important role for understanding past seasonal climate with their inherent annual time resolution and within-year seasonal patterns. We propose to use functional data analysis methods to extract the relevant information with respect to climate reconstruction from the rich but complex information in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates. In particular we analyze varved sediment from lake Kassjon in northern Sweden, covering the past 6400 years. The properties of each varve reflect to a large extent weather conditions and internal biological processes in the lake the year that the varve was deposited. Functional clustering is used to group the seasonal patterns into different types, that can be associated with different weather conditions. The seasonal patterns were described by penalized splines and clustered by the k-means algorithm, after alignment. The observed (within-year) variability in the data was used to determine the degree of smoothing for the penalized spline approximations. The resulting clusters and their time dynamics show great potential for seasonal climate interpretation, in particular for winter climate changes.

  • 29.
    Arnqvist, Per
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sjösted de Luna, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Model based functional clustering of varved lake sedimentsManuscript (preprint) (Other academic)
    Abstract [en]

    Climate and environmental changes are today widely discussed, and in particular the impact of human activity. To understand variations in past climate over longer time periods, historical documents, year rings from trees, ice cores from glaciers as well as lake and sea sediments are being used.In this paper we introduce a model based functional cluster analysis, giving us possibility to use both the functional form and covariates in our analysis. It also allow us to model the dependency of the chosen basis coefficients and the covariates. We also allow for different covariance structure within each cluster and give suggestions on how to determine how many clusters to use.In particular we analyze varved sediment from lake Kassjön (N Sweden) which cover more than 6400 years.

  • 30.
    Arvidsson, Dan
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Westerlund, Fredrik
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Fjärranalys av skog med multivariata modeller2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 31.
    Arvidsson, Per
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Snickars, Samuel
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Molekylär klassificering av tjocktarmscancer: PAM-klusteranalys för identifiering av undergrupper2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The main objective of this study is to divide a number of colorectal cancer cases into subgroups based on their molecular features using cluster analysis. The data used is supplied by a research group at Pathology, the Department of Medical Biosciences, Umeå University, and consists, after some preparation, of 455 observations which is a larger data set than many similar studies. The molecular variables that the clustering is based on are CIMP (CpG Island Methylator Phenotype), MSI (Micro Satellite Instability), BRAF- and KRAS-mutations. These are categorical variables and consequently the clustering method used is PAM (Partitioning Around Medoids) which is particularly useful with data on diverse variable level. The final analysis results in four subgroups that are represented by different combinations of attributes on the aforementioned variables. The disparity between the clusters are then evaluated by, for instance, comparing the survival time for their pertaining patients and it appears that two of the clusters are significantly different in this aspect. Other patient related and tumor specific characteristics are also linked with the separate cancer types and tested if they occur in varying extent. The locations of the tumors in the colon are for instance significantly different between the groups. Cluster analyses are exploratory tools so the choice of useful variables and subsequent interpretation of the results can be complicated and require relevant subject knowledge.

  • 32. Atroshi, Isam
    et al.
    Lyrén, Per-Erik
    Umeå University, Faculty of Social Sciences, Department of applied educational science.
    Gummesson, Christina
    Responsiveness of the 6-item CTS symptoms scale in carpal tunnel syndrome2010Conference paper (Other academic)
  • 33.
    Atroshi, Isam
    et al.
    Department of Clinical Sciences, Lund University, Lund, Sweden.
    Lyrén, Per-Erik
    Umeå University, Faculty of Social Sciences, Department of Educational Measurement.
    Gummesson, Christina
    Department of Health Sciences, Division of Physiotherapy, Lund University, 22100 Lund, Sweden.
    The 6-item CTS symptoms scale: a brief outcomes measure for carpal tunnel syndrome2009In: Quality of Life Research, ISSN 0962-9343, E-ISSN 1573-2649, Vol. 18, no 3, p. 347-358Article in journal (Refereed)
  • 34. Atroshi, Isam
    et al.
    Lyrén, Per-Erik
    Umeå University, Faculty of Social Sciences, Department of applied educational science.
    Ornstein, Ewald
    Gummesson, Christina
    Responsiveness of the 6-item CTS Symptoms Scale as a brief outcome measure in carpal tunnel syndrome2010Conference paper (Refereed)
  • 35.
    Avelin, Benny
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nyström, Kaj
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Boundary estimates for solutions to operators of p-Laplace type with lower order terms2011In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 250, no 1, p. 264-291Article in journal (Refereed)
    Abstract [en]

    In this paper we study the boundary behavior of solutions to equations of the form∇⋅A(x,∇u)+B(x,∇u)=0, in a domain ΩRn, assuming that Ω is a δ-Reifenberg flat domain for δ sufficiently small. The function A is assumed to be of p-Laplace character. Concerning B, we assume that |∇ηB(x,η)|⩽c|η|p−2, |B(x,η)|⩽c|η|p−1, for some constant c, and that B(x,η)=|η|p−1B(x,η/|η|), whenever xRn, ηRn∖{0}. In particular, we generalize the results proved in J. Lewis et al. (2008) [12] concerning the equation ∇⋅A(x,∇u)=0, to equations including lower order terms.

  • 36.
    Baek, Seung Ki
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Choi, Jung-Kyoo
    Kim, Beom Jun
    Dworkin's Paradox2012In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 7, no 6, p. e38529-Article in journal (Refereed)
    Abstract [en]

    How to distribute welfare in a society is a key issue in the subject of distributional justice, which is deeply involved with notions of fairness. Following a thought experiment by Dworkin, this work considers a society of individuals with different preferences on the welfare distribution and an official to mediate the coordination among them. Based on a simple assumption that an individual's welfare is proportional to how her preference is fulfilled by the actual distribution, we show that an egalitarian preference is a strict Nash equilibrium and can be favorable even in certain inhomogeneous situations. These suggest how communication can encourage and secure a notion of fairness.

  • 37. Banerjee, Malay
    et al.
    Zhang, Lai
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Time delay can enhance spatio-temporal chaos in a prey-predator model2016In: Ecological Complexity: An International Journal on Biocomplexity in the Environment and Theoretical Ecology, ISSN 1476-945X, E-ISSN 1476-9840, Vol. 27, p. 17-28Article in journal (Refereed)
    Abstract [en]

    In this paper we explore how the time delay induced Hopf-bifurcation interacts with Turing instability to determine the resulting spatial patterns. For this study, we consider a delayed prey-predator model with Holling type-II functional response and intra-specific competition among the predators. Analytical criteria for the delay induced Hopf-bifurcation and for the delayed spatio-temporal model are provided with numerical example to validate the analytical results. Exhaustive numerical simulation reveals the appearance of three types of stationary patterns, cold spot, labyrinthine, mixture of stripe-spot and two non-stationary patterns, quasi-periodic and spatio-temporal chaotic patterns. The qualitative features of the patterns for the non-delayed and the delayed spatio-temporal model are the same but their occurrence is solely controlled by the temporal parameters, rate of diffusivity and magnitude of the time delay. It is evident that the magnitude of time delay parameter beyond the Hopf-bifurcation threshold mostly produces spatio-temporal chaotic patterns. 

  • 38. Barban, Nicola
    et al.
    de Luna, Xavier
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.
    Lundholm, Emma
    Svensson, Ingrid
    Billari, F C
    Causal Effects of the Timing of Life-course Events: Age at Retirement and Subsequent Health2017In: Sociological Methods & Research, ISSN 0049-1241, E-ISSN 1552-8294Article in journal (Refereed)
  • 39.
    Barkhordari, Mahnaz
    et al.
    Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran.
    Padyab, Mojgan
    Umeå University, Faculty of Social Sciences, Centre for Demographic and Ageing Research (CEDAR).
    Hadaegh, Farzad
    Prevention of Metabolic Disorders Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran.
    Azizi, Fereidoun
    Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran.
    Bozorgmanesh, Mohammadreza
    Prevention of Metabolic Disorders Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, IR Iran.
    Stata Modules for Calculating Novel Predictive Performance Indices for Logistic Models2016In: International Journal of Endocrinology and Metabolism, ISSN 1726-9148, Vol. 14, no 1, article id e26707Article in journal (Refereed)
    Abstract [en]

    Background: Prediction is a fundamental part of prevention of cardiovascular diseases (CVD). The development of prediction algorithms based on the multivariate regression models loomed several decades ago. Parallel with predictive models development, biomarker researches emerged in an impressively great scale. The key question is how best to assess and quantify the improvement in risk prediction offered by new biomarkers or more basically how to assess the performance of a risk prediction model. Discrimination, calibration, and added predictive value have been recently suggested to be used while comparing the predictive performances of the predictive models’ with and without novel biomarkers.Objectives: Lack of user-friendly statistical software has restricted implementation of novel model assessment methods while examining novel biomarkers. We intended, thus, to develop a user-friendly software that could be used by researchers with few programming skills.Materials and Methods: We have written a Stata command that is intended to help researchers obtain cut point-free and cut point-based net reclassification improvement index and (NRI) and relative and absolute Integrated discriminatory improvement index (IDI) for logistic-based regression analyses.We applied the commands to a real data on women participating the Tehran lipid and glucose study (TLGS) to examine if information of a family history of premature CVD, waist circumference, and fasting plasma glucose can improve predictive performance of the Framingham’s “general CVD risk” algorithm.Results: The command is addpred for logistic regression models.Conclusions: The Stata package provided herein can encourage the use of novel methods in examining predictive capacity of ever-emerging plethora of novel biomarkers.

  • 40.
    Bayisa, Fekadu
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Kuljus, Kristi
    Institute of Mathematics and Statistics, University of Tartu, Tartu, Estonia.
    Johansson, Adam
    Umeå University, Faculty of Medicine, Department of Radiation Sciences.
    Bolin, David
    Department of Mathematical Sciences, Chalmers and University of Gothenburg, Gothenburg, Sweden.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Prediction of CT images from MR images with hidden Markov and random field models2016In: Proceedings of the 8th International Workshop on Spatio-Temporal Modelling / [ed] A. Iftimi, J. Mateu and F. Montes, 2016, p. 163-163Conference paper (Other academic)
  • 41.
    Bayisa, Fekadu L.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Liu, Xijia
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Garpebring, Anders
    Umeå University, Faculty of Medicine, Department of Radiation Sciences.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Computed Tomography Image Estimation by Statistical Learning MethodsManuscript (preprint) (Other academic)
    Abstract [en]

    There is increasing interest in computed tomography (CT) image estimations from magnetic resonance (MR) images. The estimated CT images canbe utilised for attenuation correction, patient positioning, and dose planningin diagnostic and radiotherapy workflows. This study presents a statisticallearning method for CT image estimation. We have used predefined tissuetype information in a Gaussian mixture model to explore the estimation.The performance of our method was evaluated using cross-validation on realdata. In comparison with the existing model-based CT image estimationmethods, the proposed method has improved the estimation, particularly inbone tissues. Evaluation of our method shows that it is a promising methodto generate CT image substitutes for the implementation of fully MR-basedradiotherapy and PET/MRI applications.

  • 42.
    Bayisa, Fekadu Lemessa
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Statistical methods in medical image estimation and sparse signal recovery2018Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis presents work on methods for the estimation of computed tomography (CT) images from magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. The study also demonstrates sparse signal recovery method, which is an intermediate method for magnetic resonance image reconstruction. The thesis consists of four articles. The first three articles are concerned with developing statistical methods for the estimation of CT images from MR images. We formulated spatial and non-spatial models for CT image estimation from MR images, where the spatial models include hidden Markov model (HMM) and hidden Markov random field model (HMRF) while the non-spatial models incorporate Gaussian mixture model (GMM) and skewed-Gaussian mixture model (SGMM). The statistical models are estimated via a maximum likelihood approach using the EM-algorithm in GMM and SGMM, the EM gradient algorithm in HMRF and the Baum–Welch algorithm in HMM. We have also examined CT image estimation using GMM and supervised statistical learning methods. The performance of the models is evaluated using cross-validation on real data. Comparing CT image estimation performance of the models, we have observed that GMM combined with supervised statistical learning method has the best performance, especially on bone tissues. The fourth article deals with a sparse modeling in signal recovery. Using spike and slab priors on the signal, we formulated a sparse signal recovery problem and developed an adaptive algorithm for sparse signal recovery. The developed algorithm has better performance than the recent iterative convex refinement (ICR) algorithm. The methods introduced in this work are contributions to the lattice process and signal processing literature. The results are an input for the research on replacing CT images by synthetic or pseudo-CT images, and for an efficient way of recovering sparse signal.

  • 43.
    Bayisa, Fekadu
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Model-based Estimation of Computed Tomography Images2017Conference paper (Other academic)
  • 44.
    Bayisa, Fekadu
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Model-based Estimation of Computed Tomography Images2017Manuscript (preprint) (Other academic)
    Abstract [en]

    There is a growing interest to get a fully MR based radiotherapy. The most important development needed is to obtain improved bone tissue estimation. Existing model-based methods have performed poorly on bone tissues. This paper aims to obtainimproved estimation of bone tissues. Skew-Gaussian mixture model (SGMM) isproposed to further investigate CT image estimation from MR images. The estimation quality of the proposed model is evaluated using leave-one-out cross-validation method on real data. In comparison with the existing model-based approaches, the approach utilized in this paper outperforms in estimation of bone tissues, especiallyon dense bone tissues.

  • 45.
    Bayisa, Fekadu
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zhou, Zhiyong
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Cronie, Ottmar
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Adaptive algorithm for sparse signal recovery2018Manuscript (preprint) (Other academic)
    Abstract [en]

    Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priorsresults in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization problems involve either simplifying assumptions, relaxations or high computational expenses. We propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the presented optimization problem. The algorithm is based on the one-to-onemapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternatingdirection method of multipliers to recover the signal corresponding to the updated support. Experiments on synthetic data and real-world images show that the proposed AADMM algorithm provides superior performance and is computationally cheaper, compared to the recently developed iterative convex refinement (ICR) algorithm.

  • 46. Bech, Morten L
    et al.
    Bergstrom, Carl T
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Garratt, Rodney J
    Mapping change in the overnight money market2015In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 424, p. 44-51Article in journal (Refereed)
    Abstract [en]

    We use an information-theoretic approach to describe changes in lending relationships between financial institutions around the time of the Lehman Brothers failure. Unlike previous work that conducts maximum likelihood estimation on undirected networks our analysis distinguishes between borrowers and lenders and looks for broader lending relationships (multi-bank lending cycles) that extend beyond the immediate counter-parties. We detect significant changes in lending patterns following implementation of the Interest on Required and Excess Reserves policy by the Federal Reserve in October 2008. Analysis of micro-scale rates of change in the data suggests these changes were triggered by the collapse of Lehman Brothers a few weeks before.

  • 47. Behme, Anita
    et al.
    Bondesson, Lennart
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A class of scale mixtures of Gamma(k)-distributions that are generalized gamma convolutions2017In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 23, no 1, p. 773-787Article in journal (Refereed)
    Abstract [en]

    Let k > 0 be an integer and Y a standard Gamma(k) distributed random variable. Let X be an independent positive random variable with a density that is hyperbolically monotone (HIM) of order k. Then Y . X and Y/X both have distributions that are generalized gamma convolutions (GGCs). This result extends a result of Roynette et al. from 2009 who treated the case k = 1 but without use of the HM-concept. Applications in excursion theory of diffusions and in the theory of exponential functionals of Levy processes are mentioned.

  • 48.
    Belyaev, Yu. K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    This issue is devoted to the memory of Boris Vladimirovich Gnedenko2014In: Markov Processes and Related Fields, ISSN 1024-2953, Vol. 20, no 3, p. 385-389Article in journal (Refereed)
  • 49.
    Belyaev, Yu.K.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Rydén, Patrik
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On Non-Parametric Estimation of Poission Point Processes Related to Failure Stresses of Fibres2000Report (Other academic)
    Abstract [en]

    We consider statistical analysis of the reliability of fibres. The problem is to estimate the distribution law of random failure stresses of fibres (i.e. the critical level of stresses that destroy fibres) by using data obtained in a special kind of test, where several fibres are tested until they break. All new pieces resulting from this test will also be tested, if they are long enough. The test ends when all the remaining pieces are too short to be tested further. We refer to these as binary tree structured tests. We assume that the cumulative hazard function (c.h.f.) of the failure stresses of these fibres is continuous, and that the fibres are statistically identical. Under these assumptions we obtain, as the number of tested fibres increases, a strongly consistent Nelson-Aalen type estimator of the c.h.f. The functional central limit resampling theorem in Skorohod space is proved. It justifies the possibility of using resampling for estimating the accuracy of these estimators. The theorem shows that resampling can be used to asymptotically consistently estimate distribution laws of continuous functionals of the random deviations between the estimator and the true c.h.f.. For example, resampling can be used to estimate the distribution law of the maximum distance between estimators and estimands. Numerical examples suggest that resampling works well for a moderate number of tested fibres.

  • 50.
    Belyaev, Yuri
    Umeå University, Faculty of Science and Technology, Mathematical statistics.
    Application of Resampling Methods to Linear Heteroscedastic Regression with Vector Responses2004Report (Other academic)
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