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V.I.Serdobolskii

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MULTIPARAMETRIC STATISTICS

Monograph

The progress of information technologies puts forward statistical
problems that, until recently, had no mathematical solution as well as
program support. This monograph presents mathematical theory
extending the statistical method to a new sphere of applications
different by using models with number of unknown parameters so large
that it is comparable with sample size and can be much more.
This theory may be called essentially multivariate or multiparametric.
The monograph presents the summation of all previous author's
investigations carried out in the Kolmogorov asymptotics of increasing
dimension and its extension to infinite-dimensional parameter space.
A series of new more powerful multiparametric solutions are proposed
to such basic multivariate problems as the estimation,
regression, discriminant analysis, and solution to systems
of random linear equations.
These solutions have obvious theoretical and practical advantages
as compared with conventional multivariate statistical procedures:
they are applicable to data of any dimension, are always stable and
approximately unimprovable independently of distributions.
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Readers

The book will be of interest for different specialists working
in the development of theory and applications of mathematical
statistics. Mathematicians will find new classes of urgent problems
to be solved in their regions. Specialists in applied statistics
creating modern statistical software will be interested in implementing
new more powerful and more efficient algorithms proposed in the book.
Researchers applying statistical methods for practical problems
will enjoy the sense of liberation from the danger of degeneration and
instability that is characteristic for existing multivariate
statistical procedures and will get a tool for efficient treatment
of data without restrictions on the dimension.
Students and postgraduates will be interested in this book since
it will help them to get at the foremost of statistical science
and guarantee the success in their future carrier.

On the author

Foreword

Preface

CONTENTS