TY - JOUR

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

AU - Taniguchi, M.

AU - Krishnaiah, P. R.

N1 - Funding Information:
* This work is supported by Contract NOOO14-85-K-0292 of the Offtce of Naval Research and Contract F49620-85-C-0008 of the Air Force Office of Scientific Research. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copy notation hereon. + The work of this author was done at the Center for Multivariate Analysis. His permanent address is the Department of Mathematics, Hiroshima University, Hiroshima, Japan.

PY - 1987/6

Y1 - 1987/6

N2 - 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.

AB - 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.

KW - asymptotic distributions

KW - canonical correlation matrix

KW - eigenvalues

KW - sample covariance matrix

KW - time series

UR - http://www.scopus.com/inward/record.url?scp=38249033762&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249033762&partnerID=8YFLogxK

U2 - 10.1016/0047-259X(87)90083-2

DO - 10.1016/0047-259X(87)90083-2

M3 - Article

AN - SCOPUS:38249033762

VL - 22

SP - 156

EP - 176

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 1

ER -