This monograph presents the mathematical theory of statistical methods different by treating models defined by a number of para- meters comparable in magnitude with sample size and exceeding it. This branch of statistical science was developed in later decades and until lately was presented only in a series of papers in math- ematical journals, remaining practically unknown to the majority of statisticians.
The first attempt to sum up these investigations has been made in the author’s previous monograph “Multivariate Statistical Anal- ysis. A High-Dimensional Approach,” Kluwer Academic Publish- ers, 2000.
The proposed new monograph is different in that it pays more attention to fundamentals of statistics, refinines theorems proved in the previous book, solves a number of new multiparametric prob- lems, and provides the solution of infinitely dimensional problems.
This book is written, first, for specialists in mathematical statis- tics who will find here new settings, new mathematical methods, and results of a new kind urgently required in applications. Actu- ally, a new branch of statistics is originated with new mathematical problems.