# Multiparametric Statistics

## 1st Edition

**Print ISBN:**9780444560339

**eBook ISBN:**9780080555928

**Imprint:**Elsevier Science

**Published Date:**12th September 2007

**Page Count:**334

## Description

This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.

This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution.

Mathematical theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable, but also near exact within a wide class of populations.

In the conventional situation of small dimension and large sample size these new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented by the technology described in this book.

This monograph will be of interest to a variety of specialists working w

## Key Features

- Presents original mathematical investigations and open a new branch of mathematical statistics
- Illustrates a technique for developing always stable and efficient versions of multivariate statistical analysis for large-dimensional problems
- Describes the most popular methods some near exact solutions; including algorithms of non-degenerating large-dimensional discriminant and regression analysis

## Readership

Specialists in mathematical statistics and applied statistics, statistical software engineers, students specializing in mathematical and applied statistics, researchers, and economists

## Table of Contents

Foreword Preface Chapter 1. Introduction: The Development of Multiparametric Statistics Chapter 2. Fundamental Problem of Statistics Chapter 3. Spectral Theory of Large Sample Covariance Matrices Chapter 4. Asymptitically Unimprovable Solution of Multivariate Problems Chapter 5. Multiparametric Discriminant Analysis Chapter 6. Theory of Solution to High-Order Systems of Empirical Linear Algebraic Equations Appendix References Index

## Details

- No. of pages:
- 334

- Language:
- English

- Copyright:
- © Elsevier Science 2008

- Published:
- 12th September 2007

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9780080555928

- Hardcover ISBN:
- 9780444530493

- Paperback ISBN:
- 9780444560339

## Reviews

This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters. This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution. Mathematical theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable, but also near exact within a wide class of populations. In the conventional situation of small dimension and large sample size these new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented by the technology described in this book. This monograph will be of interest to a variety of specialists working w