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  • 1.
    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)
  • 2.
    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.

  • 3.
    Belyaev, Yuri
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Application of clustered resampling methods in assessing accuracy of cross-validated estimators of cross-classification probabilities of nearest-neighbor classifiers2005Report (Other academic)
  • 4.
    Belyaev, Yuri
    Umeå University, Faculty of Science and Technology, Mathematical statistics.
    Application of Resampling Methods to Linear Heteroscedastic Regression with Vector Responses2004Report (Other academic)
  • 5.
    Belyaev, Yuri
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Gnedenko, B.V. - mathematician, researcher and teacher2006In: Reliability, Vol. 19, no 4, p. 67-71Article in journal (Refereed)
  • 6.
    Belyaev, Yuri
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Resampling for lifetime distributions2007In: Encyclopeida of Statistics in Quality and Reliability, p. 1653-1657Article in journal (Refereed)
  • 7.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Analysis of contingent valuation data with self-selected rounded WTP-intervals collected by two-steps sampling plans2011In: Abstracts of the 9th Tartu Conference on Multivariate Statistics & 20th International Workshop on Matrices and Statistics / [ed] Tönu Kollo, Kelli Sander, Ants Kaasik, University of Tartu, 2011, p. 11-12Conference paper (Other academic)
  • 8.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Application of consistent resampling to linear heteroscedastic regression2003In: Bulletin of the 54th Session of the International Statistical Institute, 2003Conference paper (Other academic)
  • 9.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Approaching sequences of random distribution laws with applications to resampling1996Report (Other academic)
  • 10.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Assessing accuracy of statistical inferences by resamplings2010In: Mathematical and Statistical Models and Methods in Reliability: Applications to Medicine, Finance, and Quality Control / [ed] V.V. Rykov, N. Balakrishnan, M.S. Nikulin, New York: Birkhäuser Verlag, 2010, p. 193-206Conference paper (Other academic)
    Abstract [en]

    Suppose that a list of explanatory variables and corresponding random responses was obtained during a series of regression experiments. The characteristic of interest is the mean value of responses considered as a regression function of corresponding values of explanatory variables. For example, if responses are failure times of tested elements, then the conditional mean value of life time given the value of explanatory variable is one of the important reliability characteristics of the tested elements. The analysis of this type of data can be realized in the framework of linear heteroscedastic regression models. Here, one of the central problems is a consistent estimation of the unknown regression function when the size of data grows unboundedly. The problems related to analysis of regression data attracted many researches, see Wu [Ann. Statist. 14, 1261–1350 (1986)]. We give an approach to consistent solution of the problems under the assumption that values of explanatory variables are real numbers and the regression function is a polynomial with unknown degree and coefficients. The selection of regression function is based on resamplings from terms in the sum of the residuals estimated by the ordinary least squares method with various values of polynomial degree. In a similar way, resamplings from the weighted estimated residuals are used for consistent estimation of the deviations distributions of estimated coefficients from their true unknown values. The consistency of applied resamplings methods holds under certain assumptions, e.g. it is assumed that the residuals distributions have uniformly integrable second moments (assumption AW 2). Given in Appendix a variant of the Central Limit Resampling Theorem is used in the proofs of Theorems 1 and 2.

  • 11.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Asymptotical properties of nonparametric point estimators based on complexly structured reliability data with right-censoring1991In: Statistics (Berlin), ISSN 0233-1888, E-ISSN 1029-4910, Vol. 22, no 4, p. 589-612Article in journal (Refereed)
    Abstract [en]

    This paper presents a general approach to nonparametric estimation of unknown distribution functions and related characteristics such as cumulative hazard functions. It is based on the notion of portions of statistical data and on the property of discertely separated distributions of statistical data General assumptions are given under which the corresponding generalized maximum likelihood estimators are consistent and their deviations have asymptotically normal distributions, if the number of portions increases to indinity.

  • 12.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Bootstrap, Resampling and Mallows Metric1995Report (Other academic)
  • 13.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Central limit theorems for m-dependent heterogeneous random variables1996Report (Other academic)
  • 14.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Comment (on the paper Singpurwalla, N. Some Cracks in the Empire of Chance)2002In: International Statistical Review, ISSN 0306-7734, E-ISSN 1751-5823, Vol. 70, no 1, p. 65-67Article in journal (Other academic)
  • 15.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Computer Intensive Methods Based on Resampling in Analysis of Reliability and Survival Data2000In: Resent Advances in Reliability, Boston: Birkhäuser Verlag, 2000, p. 195-208Chapter in book (Other academic)
  • 16.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Methoden der Wahrscheinlichkeitsrechnung und Statistik bei der Analise von Zuverlassigkeitsdaten2000Book (Other academic)
  • 17.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Methods of mathematical statistics in the reliability theory2012In: Математические методы в теории надежности: основные характеристики надежности и их статистический анализ / [ed] Belyaev, Y.K., Gnedenko, B.V. and Solovjev, A.D., Moscow: URSS Librokom , 2012, 2nd, p. 551-571Chapter in book (Other academic)
  • 18.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    My communication2003In: Bulletin of the International Statistical Institute, 50th Session of ISI, Berlin, Germany, 2003Chapter in book (Refereed)
  • 19.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    My PhD scientific supervisor - Kolmogorov, A.N. Letters of Elets State University2008In: Pedagogics, History and Theory of Mathematical Education, Vol. 17, p. 24-29Article in journal (Other academic)
  • 20.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Necessary and sufficient conditions for consistency of resampling, centre of biostochastics2003Report (Other academic)
  • 21.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Non-Parametric Estimators of Risk Functions of Tensile Strengths of Wires and Their Deviations1997In: Theory of Stochastic Processes, Vol. 3 (19), no 1-2, p. 110-120Article in journal (Refereed)
  • 22.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On the accuracy of classifiers and corresponding digital discretely colored images2002In: Theory of Probability and Mathematical Statistics. American Mathematical Society, ISSN 0094-9000, Vol. 65, p. 15-25Article in journal (Refereed)
  • 23.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On the accuracy of discretely colored maps created by classifying remotely sensed data2000Report (Other academic)
  • 24.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Statistical models and analysis of interval data collected in elicitation surveys2012In: International Conference "Probability and its applications", 2012, p. 1-2Conference paper (Other academic)
  • 25.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The reliability designbased on complexly structured data1995In: Bulletin of the International Statistical Institute, 50th Session of ISI, Beijing, China, 1995, , p. 2p. 81-82Chapter in book (Refereed)
  • 26.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Vivid recollections on A.N. Kolmogorov2006In: Kolmogorov in Recollections of his PhD Students, Moscow Centre of Mathematical Education , 2006, p. 100-103Chapter in book (Other academic)
  • 27.
    Belyaev, Yuri K
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Hajiyev, A.
    Resampling methods in selection of linear heteroscedastic regression models with increasing numbers of unknown parameters2006In: Plenary papers of the International Conference "Problems of Cybernetics  and Informatics", Vol 2, Baku, 2006, p. 7-10Conference paper (Other academic)
  • 28.
    Belyaev, Yuri K
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Håkansson, C
    Kriström, Bengt
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Economics.
    Rounding it up! Interval and open ended valuation questions.2009Report (Other academic)
  • 29.
    Belyaev, Yuri K.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Swedish University of Agricultural Sciences, Umeå, Sweden.
    Kriström, B.
    Umeå University, Faculty of Social Sciences, Centre for Environmental and Resource Economics (CERE). Swedish University of Agricultural Sciences, Umeå, Sweden.
    Analysis of contingent valuation data with self-selected rounded WTP-intervals collected by two-steps sampling plans2013In: Multivariate Statistics: Theory and Applications / [ed] Tonu Kollo, World Scientific, 2013, p. 48-60Conference paper (Other academic)
  • 30.
    Belyaev, Yuri K
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Kriström, Bengt
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Economics.
    Approach to analysis of self-selected interval data2010Report (Other academic)
  • 31.
    Belyaev, Yuri K
    et al.
    Department of forest economics, SLU.
    Kriström, Bengt
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Economics. CERE, Centre for environmental and resource economics, SLU.
    Two-step approach to self-selected interval data in elicitation surveys2012Report (Other academic)
  • 32.
    Belyaev, Yuri K
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nilsson, Leif
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On consistency of maximum likelihood estimators based on resampled data2000Report (Other academic)
  • 33.
    Belyaev, Yuri K
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nilsson, Leif
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Parametric maximum likelihood estimators and resampling1997Report (Other academic)
  • 34.
    Belyaev, Yuri K.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nosco, V.P.
    Basic Notions and Exercises of Mathematical Statistics1998Book (Refereed)
  • 35.
    Belyaev, Yuri 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.
    Non-parametric estimators of the distribution of tensile strengths of wires1997Report (Other academic)
  • 36.
    Belyaev, Yuri K
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Seleznjev, Oleg
    Moscow state university.
    Approaching in distribution with applications to resampling of stochastic processes2000In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 27, no 2, p. 371-384Article in journal (Refereed)
    Abstract [en]

    We introduce the notion of weak approaching and conditionally weak approaching sequences of random processes. This notion generalizes the conventional weak convergence, and has been proposed for real valued random variables in Belyaev (1995). Some of the standard tools for an investigation of the behaviour of weak approaching sequences of random elements in metric spaces are developed. The spaces of smoothed and right-continuous functions with left-hand limits are considered. This technique allows us to use the resampling approach for an evaluation of distributions of continuous functionals on realizations of sum of an increasing number of independent random processes. Two numerical examples are presented for such functionals as supremum and number of level crossings.

  • 37.
    Belyaev, Yuri K
    et al.
    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.
    Resamplings theorems for vector valued heterogeneous random variables1997Report (Other academic)
  • 38.
    Belyaev, Yuri K
    et al.
    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.
    Weakly approaching sequences of random distributions2000Report (Refereed)
    Abstract [en]

    We introduce the notion of weakly approaching sequences of distributions, which is a generalization of the well-known concept of weak convergence of distributions. The main difference is that the suggested notion does not demand the existence of a limit distribution. A similar definition for conditional (random) distributions is presented. Several properties of weakly approaching sequences are given. The tightness of some of them is essential. The Cramér-Lévy continuity theorem for weak convergence is generalized to weakly approaching sequences of (random) distributions. It has several applications in statistics and probability. A few examples of applications to resampling are given.

  • 39.
    Belyaev, Yuri
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Sjöstedt, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Resampling from independent heterogeneous random variables with varying mean values1997In: Theory of Stochastic Processes, ISSN 0095-7380, Vol. 3, no 19, p. 121-131Article in journal (Refereed)
  • 40. Ekström, Magnus
    et al.
    Belyaev, Y.K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    On the Estimation of the Distribution of Sample Means Based on Non-Stationary Spatial Data2001Report (Other academic)
  • 41. Gnedenko, Boris Vladimirovič
    et al.
    Belyaev, Jurij Konstantinovič
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Solovʹev, Aleksandr Dmitrievič
    Mathematical methods in the reliability theory2014 (ed. 2nd)Book (Refereed)
  • 42.
    Källberg, David
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Belyaev, Yuri
    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.
    A moment-distance hybrid method for estimating a mixture of two symmetric densities2018In: Modern Stochastics: Theory and Applications, ISSN 2351-6054, Vol. 5, no 1, p. 1-36Article in journal (Refereed)
    Abstract [en]

    In clustering of high-dimensional data a variable selection is commonly applied to obtain an accurate grouping of the samples. For two-class problems this selection may be carried out by fitting a mixture distribution to each variable. We propose a hybrid method for estimating a parametric mixture of two symmetric densities. The estimator combines the method of moments with the minimum distance approach. An evaluation study including both extensive simulations and gene expression data from acute leukemia patients shows that the hybrid method outperforms a maximum-likelihood estimator in model-based clustering. The hybrid estimator is flexible and performs well also under imprecise model assumptions, suggesting that it is robust and suited for real problems.

  • 43.
    Lindkvist, Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A class of nonparametric tests in the competing riscs model when comparing two samples1995Report (Other academic)
  • 44.
    Lindkvist, Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Asymptotic Properties of Estimators in a Model of Life Data with Warnings2001Report (Other academic)
  • 45.
    Lindkvist, Håkan
    et al.
    Center of Biostatistics, Department of Forest Resource Management and Geomatics, Swedish University of Agricultural Sciences , Umeå, Sweden.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Asymptotic properties of estimators in a model of life data with warnings2004In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 34, no 2, p. 461-474Article in journal (Refereed)
    Abstract [en]

    We consider a model where elements of a single type are life tested. All elements are observed up to the time of their failures or censorings. Three types of events are possible to observe during life testing for each element: failure, censoring, and warning, where a warning can only be observed before a failure or before censoring has occurred. It is essential to know if warnings influence subsequent failures. Two subsets of data are simultaneously considered: the first consisting of only the times of the first occurrences of failure, censoring, or warning, and the second consisting of the times for those elements where warnings occurred before failures or censorings. The first subset belongs to the competing risks model, and the second consists of left-truncated data. Estimators of the cumulative hazard function before and after warnings are derived and proved to be consistent, with asymptotic normal distributions. A null hypothesis where the cumulative hazard functions before and after warnings are proportional and a corresponding alternative hypothesis that they are not proportional are defined. Under this null hypothesis an estimator for the constant of proportionality is derived and showed to be strongly consistent. Martingale techniques are used and numerical examples are provided.

  • 46.
    Lindkvist, Håkan
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Belyaev, Yuri K
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Testing goodness of fit for life data with warnings1996Report (Other academic)
  • 47.
    Nilsson, Leif
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Belyaev, Yuri K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Application of resampling to exponential and logistic regression1998Report (Other academic)
  • 48.
    patrik, Rydén
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Källberg, David
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Belyaev, Yu. K.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The HRD-Algorithm: a general method for parametric estimation of two-component mixture models2017In: Lecture Notes in Computer Science, ISSN 978-3-319-71504-9, Vol. 10684, p. 497-508Article in journal (Refereed)
    Abstract [en]

    We introduce a novel approach to estimate the parameters of a mixture of two distributions. The method combines a grid approach with the method of moments and can be applied to a wide range of two-component mixture models. The grid approach enables the use of parallel computing and the method can easily be combined with resampling techniques. We derive the method for the special cases when the data are described by the mixture of two Weibull distributions or the mixture of two normal distributions, and apply the method on gene expression data from 409 ER+" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ER+ER+ breast cancer patients.

  • 49.
    Wiklund, Fredrik
    et al.
    Umeå University, Faculty of Medicine, Department of Radiation Sciences, Oncology.
    Eklund, Johan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Belyaev, Yuri
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Prediction of cancer incidence1998Report (Other academic)
    Abstract [en]

    In this paper a method for predicting future number of cancer diagnoses is derived. The method is based on estimation of the cumulative hazard of cancer diagnosis and cumulative hazard of population mortality. The estimation of cancer hazard is done non-parametrically, while the population death hazard is assumed to follow the Gompertz-Makeham distribution. The prediction is based on the assumption that cancer incidence and population mortality in the prediction intervals are derived. Also, prediction intervals, based on non-parametric bootstrap, are presented. The method is applied to predict number of colon cancer diagnoses among females in the northern part of Sweden. It has shown to detect and adjust for changes in population age structure, and to provide good predictions in situation where the cancer incidence and population mortality are stable during the prediction period.

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