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

Masanobu Taniguchi, P. R. Krishnaiah

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let S = (1/n) Σt=1 n 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
Externally publishedYes

Fingerprint

Canonical Correlation
Sample Covariance Matrix
Multivariate Time Series
Correlation Matrix
Covariance matrix
Asymptotic distribution
Asymptotic Expansion
Time series
Eigenvalue
Stationary Gaussian Process
Multivariate Normal
Random Vector
Identically distributed
Signal Processing
Signal processing
Zero
Canonical correlation
Asymptotic expansion
Correlation matrix
Eigenvalues

Keywords

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

ASJC Scopus subject areas

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

Cite this

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T1 - Asymptotic distributions of functions of the eigenvalues of sample covariance matrix and canonical correlation matrix in multivariate time series

AU - Taniguchi, Masanobu

AU - Krishnaiah, P. R.

PY - 1987

Y1 - 1987

N2 - Let S = (1/n) Σt=1 n 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.

AB - Let S = (1/n) Σt=1 n 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.

KW - asymptotic distributions

KW - canonical correlation matrix

KW - eigenvalues

KW - sample covariance matrix

KW - time series

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