Asymptotic distributions of functions of the eigenvalues of sample covariance matrix and canonical correlation matrix in multivariate time series

M. Taniguchi, P. R. Krishnaiah

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let S = (1/n) Σt=1n X(t) X(t)′, where X(1), ..., X(n) are p × 1 random vectors with mean zero. When X(t) (t = 1, ..., n) are independently and identically distributed (i.i.d.) as multivariate normal with mean vector 0 and covariance matrix Σ, many authors have investigated the asymptotic expansions for the distributions of various functions of the eigenvalues of S. In this paper, we will extend the above results to the case when {X(t)} is a Gaussian stationary process. Also we shall derive the asymptotic expansions for certain functions of the sample canonical correlations in multivariate time series. Applications of some of the results in signal processing are also discussed.

Original languageEnglish
Pages (from-to)156-176
Number of pages21
JournalJournal of Multivariate Analysis
Volume22
Issue number1
DOIs
Publication statusPublished - 1987 Jun
Externally publishedYes

Keywords

  • asymptotic distributions
  • canonical correlation matrix
  • eigenvalues
  • sample covariance matrix
  • time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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