### Abstract

Let S = (1/n) Σ_{t=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 language | English |
---|---|

Pages (from-to) | 156-176 |

Number of pages | 21 |

Journal | Journal of Multivariate Analysis |

Volume | 22 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1987 |

Externally published | Yes |

### Fingerprint

### 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

**Asymptotic distributions of functions of the eigenvalues of sample covariance matrix and canonical correlation matrix in multivariate time series.** / Taniguchi, Masanobu; Krishnaiah, P. R.

Research output: Contribution to journal › Article

*Journal of Multivariate Analysis*, vol. 22, no. 1, pp. 156-176. https://doi.org/10.1016/0047-259X(87)90083-2

}

TY - JOUR

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

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

VL - 22

SP - 156

EP - 176

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 1

ER -