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Belyaev, Yu. K.

Open this publication in new window or tab >>A moment-distance hybrid method for estimating a mixture of two symmetric densities### Källberg, David

### Belyaev, Yuri

### Rydén, Patrik

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##### Abstract [en]

##### 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 ()
#####

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##### Funder

Swedish Research Council, 340-2013-5185
Available from: 2018-02-08 Created: 2018-02-08 Last updated: 2018-09-19Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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.

Open this publication in new window or tab >>The HRD-Algorithm: a general method for parametric estimation of two-component mixture models### patrik, Rydén

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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.
#####

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##### Funder

Swedish Research Council, 340-2013-5185
Available from: 2018-02-08 Created: 2018-02-08 Last updated: 2018-10-15Bibliographically approved

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.

Open this publication in new window or tab >>Mathematical methods in the reliability theory### Gnedenko, Boris Vladimirovič

### Belyaev, Jurij Konstantinovič

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Solovʹev, Aleksandr Dmitrievič

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##### 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)
#####

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##### Note

OCLC Number: 898769148; eBook; Elsevier Science, 2014

Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2018-06-07Bibliographically approvedOpen this publication in new window or tab >>This issue is devoted to the memory of Boris Vladimirovich Gnedenko### Belyaev, Yu. K.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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 ()
#####

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Available from: 2015-02-04 Created: 2015-01-27 Last updated: 2018-06-07Bibliographically approved

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### Belyaev, Yuri K.

### Kriström, B.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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
#####

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Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2019-05-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Swedish University of Agricultural Sciences, Umeå, Sweden.

Umeå University, Faculty of Social Sciences, Centre for Environmental and Resource Economics (CERE). Swedish University of Agricultural Sciences, Umeå, Sweden.

Open this publication in new window or tab >>Methods of mathematical statistics in the reliability theory### Belyaev, Yuri K

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 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)
#####

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##### 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 approvedOpen this publication in new window or tab >>Statistical models and analysis of interval data collected in elicitation surveys### Belyaev, Yuri K

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 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
#####

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Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved

Open this publication in new window or tab >>Two-step approach to self-selected interval data in elicitation surveys### Belyaev, Yuri K

### Kriström, Bengt

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##### 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)
#####

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Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved

Department of forest economics, SLU.

Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Economics. CERE, Centre for environmental and resource economics, SLU.

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### Belyaev, Yuri K

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 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
#####

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Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved

Open this publication in new window or tab >>Approach to analysis of self-selected interval data### Belyaev, Yuri K

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Kriström, Bengt

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 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)
#####

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Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2018-06-08Bibliographically approved

Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Economics.