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  • 1. Alloyarova, Roza
    et al.
    Nikulin, Mikhail
    Pya, Natalya
    Voinov, Vassilly
    The Power-Generalized Weibull probability distribution and its use in survival analysis2007Ingår i: Communications in Dependability and Quality Management, Vol. 10, nr 1, s. 5-15Artikel i tidskrift (Refereegranskat)
  • 2. Fasiolo, Matteo
    et al.
    Pya, Natalya
    Wood, Simon N.
    A Comparison of Inferential Methods for Highly Nonlinear State Space Models in Ecology and Epidemiology2016Ingår i: Statistical Science, ISSN 0883-4237, E-ISSN 2168-8745, Vol. 31, nr 1, s. 96-118Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Highly nonlinear, chaotic or near chaotic, dynamic models are important in fields such as ecology and epidemiology: for example, pest species and diseases often display highly nonlinear dynamics. However, such models are problematic from the point of view of statistical inference. The defining feature of chaotic and near chaotic systems is extreme sensitivity to small changes in system states and parameters, and this can interfere with inference. There are two main classes of methods for circumventing these difficulties: information reduction approaches, such as Approximate Bayesian Computation or Synthetic Likelihood, and state space methods, such as Particle Markov chain Monte Carlo, Iterated Filtering or Parameter Cascading. The purpose of this article is to compare the methods in order to reach conclusions about how to approach inference with such models in practice. We show that neither class of methods is universally superior to the other. We show that state space methods can suffer multimodality problems in settings with low process noise or model misspecification, leading to bias toward stable dynamics and high process noise. Information reduction methods avoid this problem, but, under the correct model and with sufficient process noise, state space methods lead to substantially sharper inference than information reduction methods. More practically, there are also differences in the tuning requirements of different methods. Our overall conclusion is that model development and checking should probably be performed using an information reduction method with low tuning requirements, while for final inference it is likely to be better to switch to a state space method, checking results against the information reduction approach.

  • 3. Kussainov, Arman
    et al.
    Karimova, A.
    Kussainov, S.
    Pya, Natalya
    Immediate challenges faced by the quantum computing in time series analysis2013Ingår i: Vestnik KazNU/ Physics, Vol. 1, s. 98-101Artikel i tidskrift (Refereegranskat)
  • 4.
    Kussainov, Arman
    et al.
    Al-Farabi Kazakh National University, Almaty, Republic of Kazakhstan.
    Kussainov, S. G.
    K. I. Satpaev Kazakh National Technical University, Almaty, Republic of Kazakhstan.
    Pya, N. Y.
    University of Bath, Bath, United Kingdom.
    The neutron monitor time series data communication with the quantum algorithms2013Ingår i: Izvestiya of the National Academy of Sciences of the Republic of Kazakhstan, Physical and Mathematical Series, ISSN 2518-1483, Vol. 4, nr 290, s. 13-17Artikel i tidskrift (Refereegranskat)
  • 5. Kussainov, Arman
    et al.
    Pya, Natalya
    The neutron monitor time series statistics analysis and earthquakes prediction2011Ingår i: Vestnik KazNU/ Physics, Vol. 3, nr 38, s. 53-58Artikel i tidskrift (Refereegranskat)
  • 6.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On some extensions of shape-constrained generalized additive modelling in R2024Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Regression models that incorporate smooth functions of predictor variables to explain the relationships with a response variable have gained widespread usage and proved successful in various applications. By incorporating smooth functions of predictor variables, these models can capture complex relationships between the response and predictors while still allowing for interpretation of the results. In situations where the relationships between a response variable and predictors are explored, it is not uncommon to assume that these relationships adhere to certain shape constraints. Examples of such constraints include monotonicity and convexity. The scam package for R has become a popular package to carry out the full fitting of exponential family generalized additive modelling with shape restrictions on smooths. The paper aims to extend the existing framework of shape-constrained generalized additive models (SCAM) to accommodate smooth interactions of covariates, linear functionals of shape-constrained smooths and incorporation of residual autocorrelation. The methods described in this paper are implemented in the recent version of the package scam, available on the Comprehensive R Archive Network (CRAN).

  • 7.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    scam: Shape constrained additive models. R package version 1.2-122021Övrigt (Övrigt vetenskapligt)
  • 8.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    scam: Shape constrained additive models. R package version 1.2-132022Övrigt (Övrigt vetenskapligt)
  • 9.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    scam: Shape constrained additive models. R package version 1.2-152024Övrigt (Övrigt vetenskapligt)
    Abstract [en]

    scam provides functions for generalized additive modelling under shape constraints on the component functions of the linear predictor of the GAM. Models can contain multiple shape constrained and unconstrained terms as well as bivariate smooths with double or single monotonicity.

  • 10.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    scam: Shape constrained additive models. R package version 1.2-62020Övrigt (Övrigt vetenskapligt)
  • 11.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Arnqvist, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    fdaMocca: Model-Based Clustering for Functional Data with Covariates. R package version 0.1-02021Övrigt (Övrigt vetenskapligt)
  • 12.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Arnqvist, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    fdaMocca: Model-Based Clustering for Functional Data with Covariates. R package version 0.1-12022Övrigt (Övrigt vetenskapligt)
  • 13.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Ngendangenzwa, Blaise
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lindahl, Eric
    Volvo Group Trucks Operations.
    Nilsson, Leif
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A statistical learning approach for defect detection and classification on specular carbody surfaces2019Konferensbidrag (Refereegranskat)
  • 14.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Ngendangenzwa, Blaise
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lindahl, Eric
    Volvo Group Trucks Operations.
    Nilsson, Leif
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Efficient surface finish defect detection using reduced rank spline smoothers and probabilistic classifiers2021Ingår i: Econometrics and Statistics, ISSN 2452-3062, Vol. 18, s. 89-105Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    One of the primary concerns of product quality control in the automotive industry is an automated detection of defects of small sizes on specular car body surfaces. A new statistical learning approach is presented for surface finish defect detection based on spline smoothing method for feature extraction and k-nearest neighbour probabilistic classifier. Since the surfaces are specular, structured lightning reflection technique is applied for image acquisition. Reduced rank cubic regression splines are used to smooth the pixel values while the effective degrees of freedom of the obtained smooths serve as components of the feature vector. A key advantage of the approach is that it allows reaching near zero misclassification error rate when applying standard learning classifiers. In addition, probability based performance evaluation metrics have been proposed as alternatives to the conventional metrics. The usage of those provides the means for uncertainty estimation of the predictive performance of a classifier. Experimental classification results on the images obtained from the pilot system located at Volvo GTO Cab plant in Umeå, Sweden, show that the proposed approach is much more efficient than the compared methods.

  • 15.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Ngendangenzwa, Blaise
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nilsson, Leif
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lindahl, Eric
    Volvo Group Trucks Operations.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Automated surface finish defect detection using statistical learning approach2018Konferensbidrag (Övrigt vetenskapligt)
  • 16.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Ngendangenzwa, Blaise
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nilsson, Leif
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lindahl, Eric
    Volvo Group Trucks Operations.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Defect detection and classfiication: statistical learning approach - Part II2019Rapport (Övrigt vetenskapligt)
  • 17.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Ngendangenzwa, Blaise
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nilsson, Leif
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lindahl, Eric
    Volvo Group Trucks Operations.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Defect detection and classification: statistical learning approach2018Rapport (Övrigt vetenskapligt)
  • 18.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Ngendangenzwa, Blaise
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Nilsson, Leif
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lindahl, Eric
    Volvo Group Trucks Operations.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Efficient surface finish defect detection using reduced rank spline smoothers2019Ingår i: CRoNoS & MDA 2019, 2019Konferensbidrag (Refereegranskat)
    Abstract [en]

    One of the primary concerns of product quality control in the automotive industry is an automated detection of defects of small sizes on specular car body surfaces. A new statistical learning approach is presented for surface finish defect detection based on spline smoothing method for feature extraction and k-nearest neighbor probabilistic classifier. Rather than analyzing the natural images of the car body surfaces, the deflectometry technique is applied for image acquisition. Reduced rank cubic regression splines are used to smooth the pixel values while the effective degrees of freedom of the obtained smooths serve as components of the feature vector. A key advantage of the approach is that it allows us to reach near zero misclassification error when applying standard learning classifiers. We also propose the probability based performance evaluation metrics as alternatives to the conventional metrics. The usage of those provides the means for uncertainty estimation of the predictive performance of a classifier. Experimental classification results on the images obtained from the pilot system located at Volvo cab plant in Umea, Sweden, show that the proposed approach is much more efficient than compared methods.

  • 19.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Abramowicz, Konrad
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    fiberLD: Fiber Length Determination. R package version 0.1-62019Övrigt (Övrigt vetenskapligt)
  • 20.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Abramowicz, Konrad
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    fiberLD: Fiber Length Determination. R package version 0.1-72022Övrigt (Övrigt vetenskapligt)
  • 21.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sjöstedt de Luna, Sara
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Abramowicz, Konrad
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    fiberLD: Fiber Length Determination. R package version 0.1-82024Övrigt (Övrigt vetenskapligt)
  • 22.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Voinod, Vassilly
    Makarov, Rashid
    Voinov, Yevgeniy
    nilde: Nonnegative Integer Solutions of Linear Diophantine Equations with Applications. R package version 1.1-42021Övrigt (Övrigt vetenskapligt)
  • 23.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Voinov, Vassilly
    Makarov, Rashid
    Voinov, Yevgeniy
    mvnTest: Goodness of Fit Tests for Multivariate Normality. R package version 1.1-02016Övrigt (Övrigt vetenskapligt)
  • 24.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Voinov, Vassilly
    Voinov, Yevgeniy
    nilde: Nonnegative Integer Solutions of Linear Diophantine Equations with Applications. R package version 1.1-32019Övrigt (Övrigt vetenskapligt)
  • 25.
    Pya Arnqvist, Natalya
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Wood, Simon
    A note on basis dimension selection in generalized additive modelling2016Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Two new approaches for checking the dimension of the basis functions when using penalized regression smoothers are presented. The first approach is a test for adequacy of the basis dimension based on an estimate of the residual variance calculated by differencing residuals that are neighbours according to the smooth covariates. The second approach is based on estimated degrees of freedom for a smooth of the model residuals with respect to the model covariates. In comparison with basis dimension selection algorithms based on smoothness selection criterion (GCV, AIC, REML) the above procedures are computationally efficient enough for routine use as part of model checking.

  • 26. Pya, Natalya
    et al.
    Kussainov, Arman
    On ordered categorical modelling for complex skill development2016Ingår i: Stochastic and data analysis methods and applications in statistics and demography: book 2 / [ed] James R. Bozeman, Teresa Oliveira and Christos H. Skiadas, ISAST , 2016, s. 667-686Konferensbidrag (Refereegranskat)
  • 27. Pya, Natalya
    et al.
    Schmidt, Matthias
    Incorporating shape constraints in generalized additive modelling of the height-diameter relationship for Norway spruce2016Ingår i: Forest Ecosystems, ISSN 2095-6355, E-ISSN 2197-5620, Vol. 3, artikel-id 2Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Background: Measurements of tree heights and diameters are essential in forest assessment and modelling. Tree heights are used for estimating timber volume, site index and other important variables related to forest growth and yield, succession and carbon budget models. However, the diameter at breast height (dbh) can be more accurately obtained and at lower cost, than total tree height. Hence, generalized height-diameter (h-d) models that predict tree height from dbh, age and other covariates are needed. For a more flexible but biologically plausible estimation of covariate effects we use shape constrained generalized additive models as an extension of existing h-d model approaches. We use causal site parameters such as index of aridity to enhance the generality and causality of the models and to enable predictions under projected changeable climatic conditions.

    Methods: We develop unconstrained generalized additive models (GAM) and shape constrained generalized additive models (SCAM) for investigating the possible effects of tree-specific parameters such as tree age, relative diameter at breast height, and site-specific parameters such as index of aridity and sum of daily mean temperature during vegetation period, on the h-d relationship of forests in Lower Saxony, Germany.

    Results: Some of the derived effects, e.g. effects of age, index of aridity and sum of daily mean temperature have significantly non-linear pattern. The need for using SCAM results from the fact that some of the model effects show partially implausible patterns especially at the boundaries of data ranges. The derived model predicts monotonically increasing levels of tree height with increasing age and temperature sum and decreasing aridity and social rank of a tree within a stand. The definition of constraints leads only to marginal or minor decline in the model statistics like AIC. An observed structured spatial trend in tree height is modelled via 2-dimensional surface fitting.

    Conclusions: We demonstrate that the SCAM approach allows optimal regression modelling flexibility similar to the standard GAM but with the additional possibility of defining specific constraints for the model effects. The longitudinal character of the model allows for tree height imputation for the current status of forests but also for future tree height prediction.

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  • 28. Pya, Natalya
    et al.
    Wood, Simon N.
    Shape constrained additive models2015Ingår i: Statistics and computing, ISSN 0960-3174, E-ISSN 1573-1375, Vol. 25, nr 3, s. 543-559Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A framework is presented for generalized additive modelling under shape constraints on the component functions of the linear predictor of the GAM. We represent shape constrained model components by mildly non-linear extensions of P-splines. Models can contain multiple shape constrained and unconstrained terms as well as shape constrained multi-dimensional smooths. The constraints considered are on the sign of the first or/and the second derivatives of the smooth terms. A key advantage of the approach is that it facilitates efficient estimation of smoothing parameters as an integral part of model estimation, via GCV or AIC, and numerically robust algorithms for this are presented. We also derive simulation free approximate Bayesian confidence intervals for the smooth components, which are shown to achieve close to nominal coverage probabilities. Applications are presented using real data examples including the risk of disease in relation to proximity to municipal incinerators and the association between air pollution and health.

    Ladda ner fulltext (pdf)
    fulltext
  • 29.
    Shcherbak, Denys
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Geometry on optimal problem2023Övrigt (Övrigt vetenskapligt)
    Abstract [en]

    We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the same time, it ensures that previously fulfilled constraints are not breached during this process. The method is based on geometrical properties of n-dimensional space and can be used on any type of linear constraints (>, =, ≥), moreover it can be used when the feasible region is non-full-dimensional.

  • 30.
    Sjöstedt de Luna, Sara
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Abramowicz, Konrad
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Non-destructive methods for assessing tree fiber length distributions in standing trees2021Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    One of the main concerns of silviculture and forest management focuses on finding fast, cost-efficient and non-destructive ways of measuring wood properties in standing trees. This paper presents an R package \verb+fiberLD+ that provides functions for estimating tree fiber length distributions in the standing tree based on increment core samples. The methods rely on increment core data measured by means of an optical fiber analyzer (OFA) or measured by microscopy. Increment core data analyzed by OFAs consist of the cell lengths of both cut and uncut fibers (tracheids) and fines (such as ray parenchyma cells) without being able to identify which cells are cut or if they are fines or fibers. The microscopy measured data consist of the observed lengths of the uncut fibers in the increment core. A censored version of a mixture of the fine and fiber length distributions is proposed to fit the OFA data, under distributional assumptions. Two choices for the assumptions of the underlying density functions of the true fiber (fine) lengths of those fibers (fines) that at least partially appear in the increment core are considered, such as the generalized gamma and the log normal densities. Maximum likelihood estimation is used for estimating the model parameters for both the OFA analyzed data and the microscopy measured data.

  • 31. Voinov, Vassilly
    et al.
    Alloyarova, Roza
    Pya Arnqvist, Natalya
    Economics and Strategic Research, Kazakhstan Institute of Management, Almaty, Kazakhstan.
    Recent achievements in modified chi-squared goodness-of-fit testing2008Ingår i: Statistical models and methods for biomedical and technical systems / [ed] Filia Vonta, Mikhail Nikulin, Nikolaos Limnios, Catherine Huber-Carol, Birkhäuser Verlag, 2008, s. 241-258Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Milestones of the theory and applications of modified chi-squared tests are briefly discussed. Recent achievements in the theory and applications (in particular in reliability and survival analysis) are considered.

  • 32. Voinov, Vassilly
    et al.
    Alloyarova, Roza
    Pya, Natalya
    A modified chi-squared goodness-of-fit test for the three-parameter Weibull distribution and its applications in reliability2008Ingår i: Mathematical methods in survival analysis, reliability and quality of life / [ed] Catherine Huber, Nikolaos Limnios, Mounir Mesbah, Mikhail Nikulin, John Wiley & Sons, 2008, s. 189-202Kapitel i bok, del av antologi (Refereegranskat)
  • 33. Voinov, Vassilly
    et al.
    Nikulin, Mikhail
    Pya, Natalya
    Kazakhstan Institute of Management, Economics and Strategic Research, Almaty, Kazakhstan.
    Independent chi-squared one distributed in the limit components of some chi-squared tests2007Ingår i: Recent advances in stochastic modelling and data analysis / [ed] Christos H. Skiadas, World Scientific, 2007, s. 243-250Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Non-parametric and parametric explicit decompositions of the classical Pearson, Pearson-Fisher, Hsuan-Robson-Mirvaliev and other tests on a sum of asymptotically independent chi-squared random variables with one degree of freedom in case of non-equiprobable cells are discussed. The parametric decompositions can be used for constructing more powerful tests, and can be considered as alternative proofs of limit theorems for some chi-squared type goodness-of-fit statistics.

  • 34. Voinov, Vassilly
    et al.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    R-software for additive partitioning of positive integers2017Ingår i: Mathematical Journal, ISSN 1682-0525, Vol. 17, nr 1, s. 69-76Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An algorithm for additive partitioning of natural numbers is considered. The approach is based on a generating function discussed in detail in 1994-1997 by Voinov and Nikulin. The approach is used for the enumeration of nonnegative integer solutions of a corresponding linear Diophantine equation. A new R-algorithm for solving the partitioning problems is presented.

  • 35. Voinov, Vassilly
    et al.
    Pya Arnqvist, Natalya
    Alloyarova, Roza
    A comparative study of some modified chi-squared tests2009Ingår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 38, nr 2, s. 355-367Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Some recent results in the theory and applications of modified chi-squared goodnessof-fit tests are briefly discussed. It seems that for the first time power of modified chi-squared type tests for the logistic and three-parameter Weibull distributions based on moment type estimators is studied. Power of different modified tests against some alternatives for equiprobable fixed or random grouping intervals, and for Neyman–Pearson classes is investigated. It is shown that power of test statistic essentially depends on the quantity of Fisher’s sample information this statistic uses. Some recommendations on implementing modified chi-squared type tests are given.

  • 36. Voinov, Vassilly
    et al.
    Pya Arnqvist, Natalya
    KIMEP University, Almaty, Kazakhstan.
    Makarov, Rashid
    Voinov, Yevgeniy
    New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study2016Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, nr 11, s. 3249-3263Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    New invariant and consistent goodness-of-fit tests for multivariate normality are introduced. Tests are based on the Karhunen–Loève transformation of a multidimensional sample from a population. A comparison of simulated powers of tests and other well-known tests with respect to some alternatives is given. The simulation study demonstrates that power of the proposed McCull test almost does not depend on the number of grouping cells. The test shows an advantage over other chi-squared type tests. However, averaged over all of the simulated conditions examined in this article, the Anderson–Darling type and the Cramer–von Mises type tests seem to be the best.

  • 37. Voinov, Vassilly
    et al.
    Pya Arnqvist, Natalya
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Voinov, Yevgeniy
    Polynomial in time nonnegative integer solutions of knapsacks and similar problems in R: P=NP?2018Ingår i: Mathematical Journal, ISSN 1682-0525, Vol. 18, nr 2, s. 47-58Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new result is the well forgotten old one"(A Russian proverb) Annotation. An R-package "nilde" [1] for the enumeration of all existing nonnegative integer solutions of linear Diophantine equations and inequalities and related problems is presented. The software uses the approach based on a generating function of Hardy and Littlewood [2] introduced in 1966 and the algorithm proposed by Voinov and Nikulin [3] in 1997. The package proves to be useful for solving 0-1, bounded and unbounded knapsacks, subset sum problems, integer linear programs, partitioning of natural numbers, etc. The main advantage of the proposed software is that it solves all the above problems in polynomial time. Numerous examples illustrate applications of the package. Strong theoretical and empirical arguments in favor of equality P=NP are presented.

  • 38. Voinov, Vassilly
    et al.
    Pya, Natalya
    A note on vector-valued goodness-of-fit tests2010Ingår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 39, nr 3, s. 452-459Artikel i tidskrift (Refereegranskat)
  • 39. Voinov, Vassilly
    et al.
    Pya, Natalya
    Makarov, Rashid
    Voinov, Yevgeniy
    Goodness-of-fit tests for two-dimensional circular normal probability distribution2012Ingår i: AFBE Journal, Vol. 5, nr 2, s. 201-218Artikel i tidskrift (Övrigt vetenskapligt)
  • 40. Wood, Simon N.
    et al.
    Pya Arnqvist, Natalya
    Safken, Benjamin
    Smoothing parameter and model selection for general smooth models2016Ingår i: Journal of the American Statistical Association, ISSN 0162-1459, E-ISSN 1537-274X, Vol. 111, nr 516, s. 1548-1563Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of model selection tools available. The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for nonexponential family responses (e.g., beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (e.g., two stage zero inflation models, and Gaussian location scale models), Cox proportional hazards models and multivariate additive models. The framework reduces the implementation of new model classes to the coding of some standard derivatives of the log-likelihood. Supplementary materials for this article are available online.

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