This paper is concerned with asymptotic distributions of functions of a sample covariance matrix under the elliptical model. Simple but useful formulae for calculating asymptotic variances and covariances of the functions are derived. Also, an asymptotic expansion formula for the expectation of a function of a sample covariance matrix is derived; it is given up to the second-order term with respect to the inverse of the sample size. Two examples are given: one of calculating the asymptotic variances and covariances of the stepdown multiple correlation coefficients, and the other of obtaining the asymptotic expansion formula for the moments of sample generalized variance.
Description
Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution - Iwashita - 1994 - Canadian Journal of Statistics - Wiley Online Library
%0 Journal Article
%1 CJS:CJS273
%A Iwashita, Toshiya
%A Siotani, Minoru
%D 1994
%I Wiley-Blackwell
%J Canadian Journal of Statistics
%K distributions elliptical multivariate statistics
%N 2
%P 273--283
%R 10.2307/3315589
%T Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution
%U http://dx.doi.org/10.2307/3315589
%V 22
%X This paper is concerned with asymptotic distributions of functions of a sample covariance matrix under the elliptical model. Simple but useful formulae for calculating asymptotic variances and covariances of the functions are derived. Also, an asymptotic expansion formula for the expectation of a function of a sample covariance matrix is derived; it is given up to the second-order term with respect to the inverse of the sample size. Two examples are given: one of calculating the asymptotic variances and covariances of the stepdown multiple correlation coefficients, and the other of obtaining the asymptotic expansion formula for the moments of sample generalized variance.
@article{CJS:CJS273,
abstract = {This paper is concerned with asymptotic distributions of functions of a sample covariance matrix under the elliptical model. Simple but useful formulae for calculating asymptotic variances and covariances of the functions are derived. Also, an asymptotic expansion formula for the expectation of a function of a sample covariance matrix is derived; it is given up to the second-order term with respect to the inverse of the sample size. Two examples are given: one of calculating the asymptotic variances and covariances of the stepdown multiple correlation coefficients, and the other of obtaining the asymptotic expansion formula for the moments of sample generalized variance.},
added-at = {2018-02-01T07:47:36.000+0100},
author = {Iwashita, Toshiya and Siotani, Minoru},
biburl = {https://www.bibsonomy.org/bibtex/21b528f765fecc6d340e00b426668df22/shabbychef},
description = {Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution - Iwashita - 1994 - Canadian Journal of Statistics - Wiley Online Library},
doi = {10.2307/3315589},
interhash = {0edf3dfc6f9b466eaa11fd92a7a5a81e},
intrahash = {1b528f765fecc6d340e00b426668df22},
issn = {1708-945X},
journal = {Canadian Journal of Statistics},
keywords = {distributions elliptical multivariate statistics},
number = 2,
pages = {273--283},
publisher = {Wiley-Blackwell},
timestamp = {2018-02-01T07:47:36.000+0100},
title = {Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution},
url = {http://dx.doi.org/10.2307/3315589},
volume = 22,
year = 1994
}