Principal components analysis for mixtures with varying concentrations
Volume 8, Issue 4 (2021), pp. 509–523
Pub. online: 12 November 2021
Type: Research Article
Open Access
Open Access
Received
14 August 2021
14 August 2021
Revised
30 October 2021
30 October 2021
Accepted
30 October 2021
30 October 2021
Published
12 November 2021
12 November 2021
Abstract
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.
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