ANALYSIS OF THE LIMITING SPECTRAL DISTRIBUTION OF LARGE DIMENSIONAL RANDOM MATRICES

被引：184

作者：

SILVERSTEIN, JW ^{[1
]}

CHOI, SI ^{[1
]}

机构：

[1] N CAROLINA STATE UNIV, RALEIGH, NC 27695 USA

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1995年 / 54卷 / 02期

关键词：

EIGENVALUES OF RANDOM MATRICES; SPECTRAL DISTRIBUTION; STIELTJES TRANSFORM;

D O I：

10.1006/jmva.1995.1058

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Results on the analytic behavior of the limiting spectral distribution of matrices of sample covariance type, studied in Marcenko and Pastur [2] and Yin [8], are derived. Through an equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and resembles root\x-x(o)\ for most cases of x(o) in the boundary of its support. A complete analysis of a way to determine its support, originally outlined in Marenko and Pastur [2], is also presented. (C) 1995 Academic Press, Inc.

引用

页码：295 / 309

页数：15

共 7 条

[1]

JOHSSON D, 1986, J MULTIVARIATE ANAL, V12, P1

[2]

Marchenko V. A., 1967, MATH USSR SB, V114, P507, DOI [10.1070/SM1967v001n04ABEH001994, DOI 10.1070/SM1967V001N04ABEH001994]

[3] THE LIMITING EIGENVALUE DISTRIBUTION OF A MULTIVARIATE F-MATRIX [J].