FOREWORD

The monograph "Multiparametric Statistics" by V.Serdobolskii presents the mathematical theory of statistical methods different by treating models defined by a number of parameters comparable in magnitude with sample size and exceeding it. This branch of statistical science was developed in latter decades and until lately was presented only in a series of papers in mathematical journals remaining practically unknown to the majority of statisticians.

The first attempt to sum up these investigations has been made in the previous author's monograph "Multivariate Statistical Analysis. A High-Dimensional Approach", Kluwer Academic Publishers, 2000.

The monograph "Multiparametric Statistics" is different by more attention to fundamentals of statistics, by refining theorems proved in the previous book, by solving a number of new multiparametric problems, and by the solution of infinitely-dimensional problems.

This book is written, first, for specialists in mathematical statistics who will find there new settings, new mathematical methods and results of a new kind urgently required in applications. Actually, a new region of statistics is originated with new mathematical problems.

Specialists in applied statistics creating statistical packages for statistical software will be interested in implementing new more efficient methods proposed in the book. Advantages of these methods are obvious: the user is liberated from the permanent uncertainty of possible degeneration of linear methods and gets approximately unimprovable algorithms whose quality does not depend on distributions.

Specialists applying statistical methods to their concrete problems will find in the book a number of always stable approximately unimprovable algorithms that will help them to solve better their scientific or economic problems.

Students and postgraduates may be interested in this book in order to get at the foremost frontier of modern statistical science that would guarantee them the success in their future carrier.