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.
A general jackknife estimator for the asymptotic covariance of moment estimators is considered in the case when the sample is taken from a mixture with varying concentrations of components. Consistency of the estimator is demonstrated. A fast algorithm for its calculation is described. The estimator is applied to construction of confidence sets for regression parameters in the linear regression with errors in variables. An application to sociological data analysis is considered.