Multiparameter Methods are the New Field in Statistics

Abstract

During the last decade statistical problems of a new kind have appeared more and more often, in which the dimensionality of observations is large, and the sample size is small or comparable with the dimensionality of observations. These problems may be characterized as multiparameter problems. The theory of multiparameter analysis, proposed by A.N.Kolmogorov and supported by the studies on the spectral theory of random matrices of V. A.Marchenko, L. A.Pastur, V. L.Girko, and others, revealed some specific phenomena appearing in statistics with a large number of weakly dependent variables. Particularly, there are stable relations between the principal parts of parameter set functions and the set of observed variables, which may be used to improve the statistical analysis. The use of these phenomena allows one to develop a thorough, always stable, and approximately optimal (irrespective of samples) versions of mostly used statistical procedures. The multiparameter versions of the discriminant analysis are of special interest.