An Introduction to Statistical Analysis of Random Arrays / V. L. Girko.

Format:

Book

Author/Creator:

Girko, V. L., author.

Language:

English

Subjects (All):

Random matrices.

Multivariate analysis.

Physical Description:

1 online resource (700 pages)

Edition:

Reprint 2018

Place of Publication:

Berlin ; Boston : De Gruyter, [2018]

Language Note:

In English.

Summary:

This book contains the results of 30 years of investigation by the author into the creation of a new theory on statistical analysis of observations, based on the principle of random arrays of random vectors and matrices of increasing dimensions. It describes limit phenomena of sequences of random observations, which occupy a central place in the theory of random matrices. This is the first book to explore statistical analysis of random arrays and provides the necessary tools for such analysis. This book is a natural generalization of multidimensional statistical analysis and aims to provide its readers with new, improved estimators of this analysis. The book consists of 14 chapters and opens with the theory of sample random matrices of fixed dimension, which allows to envelop not only the problems of multidimensional statistical analysis, but also some important problems of mechanics, physics and economics. The second chapter deals with all 50 known canonical equations of the new statistical analysis, which form the basis for finding new and improved statistical estimators. Chapters 3-5 contain detailed proof of the three main laws on the theory of sample random matrices. In chapters 6-10 detailed, strong proofs of the Circular and Elliptic Laws and their generalization are given. In chapters 11-13 the convergence rates of spectral functions are given for the practical application of new estimators and important questions on random matrix physics are considered. The final chapter contains 54 new statistical estimators, which generalize the main estimators of statistical analysis.

Contents:

Frontmatter

CONTENTS

List of basic notations and assumptions

Preface and some historical remarks

Chapter 1. Introduction to the theory of sample matrices of fixed dimension

Chapter 2. Canonical equations

Chapter 3. The First Law for the eigenvalues and eigenvectors of random symmetric matrices

Chapter 4. The Second Law for the singular values and eigenvectors of random matrices. Inequalities for the spectral radius of large random matrices

Chapter 5. The Third Law for the eigenvalues and eigenvectors of empirical covariance matrices

Chapter 6. The first proof of the Strong Circular Law

Chapter 7. Strong Law for normalized spectral functions of nonselfadjoint random matrices with independent row vectors and simple rigorous proof of the Strong Circular Law

Chapter 8. Rigorous proof of the Strong Elliptic Law

Chapter 9. The Circular and Uniform Laws for eigenvalues of random nonsymmetric complex matrices with independent entries

Chapter 10. Strong V-Law for eigenvalues of nonsymmetric random matrices

Chapter 11. Convergence rate of the expected spectral functions of symmetric random matrices is equal to 0(n-1/2)

Chapter 12. Convergence rate of expected spectral functions of the sample covariance matrix Ȓm"(n) is equal to 0(n-1/2) under the condition m"n-1≤c<1

Chapter 13. The First Spacing Law for random symmetric matrices

Chapter 14. Ten years of General Statistical Analysis (The main G-estimators of General Statistical Analysis)

References

Index

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9783110916683

3110916681

OCLC:

1076460161