Multivariate Statistical Analysis. A High-Dimensional Approach

by V.Serdobolskii

published by "Kluwer Science Publishers" in October of 2000
ISBN 0-7923-6643-3

Mailing address:
Kluwer Academic Publishers, Sales Departement
PO BOX 17, 3300 AA, Dordrecht, The Netherlands

Site to order:

In contrast to other books on multivariate analysis retelling classical theory of the multivariate statistical analysis based on the idea of a consistency, the author develops an essentially new theoretical-decision approach to the multivariate analysis that leads to always stable approximately unimprovable distribution free methods.

This book may be of interest for specialists in mathematical statistics in universities and institutes with mathematical departments, departments of statistics, research institutes and computer centers creating and improving packages of applied statistical programs. The book can serve as a text-book for students and post-graduates studying mathematics and statistics.

The book "Multivariate Statistical Analysis. A High-Dimensional Approach" presents a new branch of mathematical statistics solving problems of construction of approximately unimprovable versions of the multivariate analysis methods such as multiparametric estimation, discriminant and regression analysis. In contrast to the traditional consistent Fisher method of statistics, the essentially multivariate technique is developed based on the decision function approach by A. Wald. For large dimension of observations comparable in magnitude with sample size, stable approximately unimprovable in some wide classes procedures depending on an arbitrary function are offered. A remarkable fact is established: for large-dimensional problems, under some weak restrictions on the variable dependence, the standard quality functions of regularized multivariate procedures prove to be independent of distributions. This opens, for the first time in the history of statistics, a possibility to construct approximately unimprovable procedures free from distributions.

Hosted by uCoz