Principal components analysis for mixtures with varying concentrations

Principal Component Analysis (PCA) is a classical technique of dimension reduction for multivariate data. When the data are a mixture of subjects from different subpopulations one can be interested in PCA of some (or each) subpopulation separately. In this paper estimators are considered for PC dire...

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Autores principales:	Olena Sugakova, Rostyslav Maiboroda
Formato:	article
Lenguaje:	EN
Publicado:	VTeX 2021
Materias:	Finite mixture model principal components mixture with varying concentrations nonparametric estimation Asymptotic normality confidence interval Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e5c2e87d921840a693dcf03bb32adde1
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id	oai:doaj.org-article:e5c2e87d921840a693dcf03bb32adde1
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spelling	oai:doaj.org-article:e5c2e87d921840a693dcf03bb32adde12021-11-17T08:47:30ZPrincipal components analysis for mixtures with varying concentrations10.15559/21-VMSTA1912351-60462351-6054https://doaj.org/article/e5c2e87d921840a693dcf03bb32adde12021-11-01T00:00:00Zhttps://www.vmsta.org/doi/10.15559/21-VMSTA191https://doaj.org/toc/2351-6046https://doaj.org/toc/2351-6054Principal Component Analysis (PCA) is a classical technique of dimension reduction for multivariate data. When the data are a mixture of subjects from different subpopulations one can be interested in PCA of some (or each) subpopulation separately. In this paper estimators are considered for PC directions and corresponding eigenvectors of subpopulations in the nonparametric model of mixture with varying concentrations. Consistency and asymptotic normality of obtained estimators are proved. These results allow one to construct confidence sets for the PC model parameters. Performance of such confidence intervals for the leading eigenvalues is investigated via simulations.Olena SugakovaRostyslav MaiborodaVTeXarticleFinite mixture modelprincipal componentsmixture with varying concentrationsnonparametric estimationAsymptotic normalityconfidence intervalApplied mathematics. Quantitative methodsT57-57.97MathematicsQA1-939ENModern Stochastics: Theory and Applications, Vol 8, Iss 4, Pp 509-523 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Finite mixture model principal components mixture with varying concentrations nonparametric estimation Asymptotic normality confidence interval Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
spellingShingle	Finite mixture model principal components mixture with varying concentrations nonparametric estimation Asymptotic normality confidence interval Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939 Olena Sugakova Rostyslav Maiboroda Principal components analysis for mixtures with varying concentrations
description	Principal Component Analysis (PCA) is a classical technique of dimension reduction for multivariate data. When the data are a mixture of subjects from different subpopulations one can be interested in PCA of some (or each) subpopulation separately. In this paper estimators are considered for PC directions and corresponding eigenvectors of subpopulations in the nonparametric model of mixture with varying concentrations. Consistency and asymptotic normality of obtained estimators are proved. These results allow one to construct confidence sets for the PC model parameters. Performance of such confidence intervals for the leading eigenvalues is investigated via simulations.
format	article
author	Olena Sugakova Rostyslav Maiboroda
author_facet	Olena Sugakova Rostyslav Maiboroda
author_sort	Olena Sugakova
title	Principal components analysis for mixtures with varying concentrations
title_short	Principal components analysis for mixtures with varying concentrations
title_full	Principal components analysis for mixtures with varying concentrations
title_fullStr	Principal components analysis for mixtures with varying concentrations
title_full_unstemmed	Principal components analysis for mixtures with varying concentrations
title_sort	principal components analysis for mixtures with varying concentrations
publisher	VTeX
publishDate	2021
url	https://doaj.org/article/e5c2e87d921840a693dcf03bb32adde1
work_keys_str_mv	AT olenasugakova principalcomponentsanalysisformixtureswithvaryingconcentrations AT rostyslavmaiboroda principalcomponentsanalysisformixtureswithvaryingconcentrations
_version_	1718425706176708608

Principal components analysis for mixtures with varying concentrations

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