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Belyaev, Yu. K.
Alternative names
Publications (10 of 49) Show all publications
Källberg, D., Belyaev, Y. & Rydén, P. (2018). A moment-distance hybrid method for estimating a mixture of two symmetric densities. Modern Stochastics: Theory and Applications, 5(1), 1-36
Open this publication in new window or tab >>A moment-distance hybrid method for estimating a mixture of two symmetric densities
2018 (English)In: Modern Stochastics: Theory and Applications, ISSN 2351-6054, Vol. 5, no 1, p. 1-36Article in journal (Refereed) Published
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.

Keywords
inference for mixtures, method of moments, minimum distance, model-based clustering
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-144644 (URN)10.15559/17-VMSTA93 (DOI)000434875200001 ()
Funder
Swedish Research Council, 340-2013-5185
Available from: 2018-02-08 Created: 2018-02-08 Last updated: 2018-09-19Bibliographically approved
patrik, R., Källberg, D. & Belyaev, Y. K. K. (2017). The HRD-Algorithm: a general method for parametric estimation of two-component mixture models. Paper presented at Analytical and Computational Methods in Probability Theory. ACMPT 2017.. Lecture Notes in Computer Science, 10684, 497-508
Open this publication in new window or tab >>The HRD-Algorithm: a general method for parametric estimation of two-component mixture models
2017 (English)In: Lecture Notes in Computer Science, ISSN 978-3-319-71504-9, Vol. 10684, p. 497-508Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Mixture models, Parameter estimation, Method of moments Grid-approach, Resampling, Cluster analysis Variable selection, High-dimensional data
National Category
Natural Sciences Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-144646 (URN)10.1007/978-3-319-71504-9_41 (DOI)
Conference
Analytical and Computational Methods in Probability Theory. ACMPT 2017.
Funder
Swedish Research Council, 340-2013-5185
Available from: 2018-02-08 Created: 2018-02-08 Last updated: 2018-10-15Bibliographically approved
Gnedenko, B. V., Belyaev, J. K. & Solovʹev, A. D. (2014). Mathematical methods in the reliability theory (2nded.). Burlington: Academic Press
Open this publication in new window or tab >>Mathematical methods in the reliability theory
2014 (English)Book (Refereed)
Alternative title[ru]
Matematičeskie metody v teorii nadežnosti
Place, publisher, year, edition, pages
Burlington: Academic Press, 2014. p. 519 Edition: 2nd
Series
Probability and mathematical statistics
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-88224 (URN)9781483263519 (ISBN)1483263517 (ISBN)
Note

OCLC Number: 898769148; eBook; Elsevier Science, 2014

Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2018-06-07Bibliographically approved
Belyaev, Y. K. K. (2014). This issue is devoted to the memory of Boris Vladimirovich Gnedenko. Markov Processes and Related Fields, 20(3), 385-389
Open this publication in new window or tab >>This issue is devoted to the memory of Boris Vladimirovich Gnedenko
2014 (English)In: Markov Processes and Related Fields, ISSN 1024-2953, Vol. 20, no 3, p. 385-389Article in journal (Refereed) Published
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-98881 (URN)000345889000001 ()
Available from: 2015-02-04 Created: 2015-01-27 Last updated: 2018-06-07Bibliographically approved
Belyaev, Y. K. & Kriström, B. (2013). Analysis of contingent valuation data with self-selected rounded WTP-intervals collected by two-steps sampling plans. In: Tonu Kollo (Ed.), Multivariate Statistics: Theory and Applications. Paper presented at The 9th Tartu Conference on Multivariate Statistics, Estonia, June 26-July 1, 2013 (pp. 48-60). World Scientific
Open this publication in new window or tab >>Analysis of contingent valuation data with self-selected rounded WTP-intervals collected by two-steps sampling plans
2013 (English)In: Multivariate Statistics: Theory and Applications / [ed] Tonu Kollo, World Scientific, 2013, p. 48-60Conference paper, Published paper (Other academic)
Place, publisher, year, edition, pages
World Scientific, 2013
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-88225 (URN)981-4449-40-7 (ISBN)
Conference
The 9th Tartu Conference on Multivariate Statistics, Estonia, June 26-July 1, 2013
Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2019-05-09Bibliographically approved
Belyaev, Y. K. (2012). Methods of mathematical statistics in the reliability theory (2nded.). In: Belyaev, Y.K., Gnedenko, B.V. and Solovjev, A.D. (Ed.), Математические методы в теории надежности: основные характеристики надежности и их статистический анализ (pp. 551-571). Moscow: URSS Librokom
Open this publication in new window or tab >>Methods of mathematical statistics in the reliability theory
2012 (Russian)In: 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)
Place, publisher, year, edition, pages
Moscow: URSS Librokom, 2012 Edition: 2nd
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-87450 (URN)978-5-397-03494-4 (ISBN)
Note

Mathematical metods in the reliability theory : the main characteristics of reliability and statistical analysis.

Prev. ed. 1965

Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved
Belyaev, Y. K. (2012). Statistical models and analysis of interval data collected in elicitation surveys. In: International Conference "Probability and its applications": . Paper presented at Probability and its applications, Moscow State Lomonosov University, June 26–30, 2012, Moscow (pp. 1-2).
Open this publication in new window or tab >>Statistical models and analysis of interval data collected in elicitation surveys
2012 (English)In: International Conference "Probability and its applications", 2012, p. 1-2Conference paper, Oral presentation with published abstract (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-87448 (URN)
Conference
Probability and its applications, Moscow State Lomonosov University, June 26–30, 2012, Moscow
Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved
Belyaev, Y. K. & Kriström, B. (2012). Two-step approach to self-selected interval data in elicitation surveys. Umeå: Umeå universitet
Open this publication in new window or tab >>Two-step approach to self-selected interval data in elicitation surveys
2012 (English)Report (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2012. p. 44
Series
CERE, Umea University & SLU, Working paper ; 2012:10
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-87452 (URN)
Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved
Belyaev, Y. K. (2011). Analysis of contingent valuation data with self-selected rounded WTP-intervals collected by two-steps sampling plans. In: Tönu Kollo, Kelli Sander, Ants Kaasik (Ed.), Abstracts of the 9th Tartu Conference on Multivariate Statistics & 20th International Workshop on Matrices and Statistics: . Paper presented at The 9th Tartu Conference on Multivariate Statistics & 20th International Workshop on Matrices and Statistics (pp. 11-12). University of Tartu
Open this publication in new window or tab >>Analysis of contingent valuation data with self-selected rounded WTP-intervals collected by two-steps sampling plans
2011 (English)In: 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, Oral presentation with published abstract (Other academic)
Place, publisher, year, edition, pages
University of Tartu, 2011
Keywords
estimable characteristics, interval rounded data, maximisation likelihood, recursion, resampling
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-87464 (URN)
Conference
The 9th Tartu Conference on Multivariate Statistics & 20th International Workshop on Matrices and Statistics
Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved
Belyaev, Y. K. & Kriström, B. (2010). Approach to analysis of self-selected interval data. Umeå: Umeå universitet
Open this publication in new window or tab >>Approach to analysis of self-selected interval data
2010 (English)Report (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2010. p. 34
Series
CERE, Umea University & SLU, Working paper ; 2010:2
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-87465 (URN)
Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved
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