The aim of this paper is to consider with the aid of the method of principal components theoretical schemes of regularization of the solution of the fundamental problems of multivariate statistics, i. e. , regression and discriminant analysis, and classification and analysis of canonical variables, with respect to degenerate (correlated) data. Such a survey is necessary also by virtue of the great interest displayed in recent years in the use of the method of principal components in applied research dealing especially with ore enrichment.