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

• Superior document: Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999
• VerfasserIn: Girko, V. L.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2018]; ©1998
• Year of Publication: 2018
• Edition: Reprint 2018
• Language: English
• Physical Description: 1 online resource (673 p.)

Table of 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