Principal components analysis for mixtures with varying concentrations

Abstract

Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Principal components analysis for mixtures with varying concentrations, Authors: Olena Sugakova, Rostyslav Maiboroda , 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.