Multiparametric statistics / by Vadim I. Serdobolskii.

Format:

Book

Author/Creator:

Serdobolskii, V.

Language:

English

Subjects (All):

Multivariate analysis.

Mathematical statistics.

Physical Description:

1 online resource (335 p.)

Edition:

1st ed.

Place of Publication:

Amsterdam ; Oxford : Elsevier, c2008.

Language Note:

English

Summary:

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

Contents:

Front Cover; Multiparametric Statistics; Copyright Page; On the Author; Table of Contents; Foreword; Preface; Chapter 1. Introduction; The Stein Effect; The Kolmogorov Asymptotics; Spectral Theory of Increasing Random Matrices; Constructing Multiparametric Procedures; Optimal Solution to Empirical Linear Equations; Chapter 2. Fundamental Problem of Statistics; 2.1. Shrinkage of Sample Mean Vectors; 2.2. Shrinkage of Unbiased Estimators; 2.3. Shrinkage of Infinite-Dimensional Vectors; 2.4. Unimprovable Component-Wise Estimation; Chapter 3. Spectral Theory of Sample Covariance Matrices

3.1. Spectral Functions of Large Sample Covariance Matrices3.2. Spectral Functions of Infinite Sample Covariance Matrices; 3.3. Normalization of Quality Functions; Chapter 4. Asymptotically Unimprovable Solution of Multivariate Problems; 4.1. Estimators of Large Inverse Covariance Matrices; 4.2. Matrix Shrinkage Estimators of Expectation Vectors; 4.3. Multiparametric Sample Linear Regression; Chapter 5. Multiparametric Discriminant Analysis; 5.1. Discriminant Analysis of Independent Variables; 5.2. Discriminant Analysis of Dependent Variables

Chapter 6. Theory of Solution to High-Order Systems of Empirical Linear Algebraic Equations6.1. The Best Bayes Solution; 6.2. Asymptotically Unimprovable Solution; Appendix: Experimental Investigation of Spectral Functions of Large Sample Covariance Matrices; 1. Theoretical Relations; 2. Numerical Experiments; References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-281-09629-6

9786611096298

0-08-055592-6

OCLC:

299750903