THE ASYMPTOTIC-DISTRIBUTION OF SINGULAR-VALUES WITH APPLICATIONS TO CANONICAL CORRELATIONS AND CORRESPONDENCE-ANALYSIS

被引：40

作者：

EATON, ML ^{[1
]}

TYLER, D ^{[1
]}

机构：

[1] RUTGERS STATE UNIV,NEW BRUNSWICK,NJ 08903

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1994年 / 50卷 / 02期

关键词：

SINGULAR VALUES; RANDOM MATRICES; ASYMPTOTIC DISTRIBUTIONS; CANONICAL CORRELATIONS; CORRESPONDENCE ANALYSIS;

D O I：

10.1006/jmva.1994.1041

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：

Let X(n), n = 1, 2, ... be a sequence of p x q random matrices, p greater-than-or-equal-to q. Assume that for a fixed p x q matrix B and a sequence of constants b(n) --> infinity, the random matrix b(n)(X(n)-B) converges in distribution to Z. Let psi(X(n)) denote the q-vector of singular values of X(n). Under these assumptions, the limiting distribution of b(n) (psi(X(n)) - psi(B)) is characterized as a function of B and of the limit matrix Z. Applications to canonical correlations and to correspondence analysis are given. (C) 1994 Academic Press, Inc.

引用

页码：238 / 264

页数：27