CIRJE-F-933 | "Tests for Covariance Matrices in High Dimension with Less Sample Size" |
Author Name | Srivastava, Muni S., Hirokazu Yanagihara and Tatsuya Kubokawa |
Date | June 2014 |
Full Paper | PDF file |
Remarks | Subsequently published in Journal of Multivariate Analysis, 130, 289-309 (2014). |
Abstract |
In this article, we propose tests for covariance matrices of high dimension with fewer observations than the dimension for a general class of distributions with positive definite covariance matrices. In one-sample case, tests are proposed for sphericity and for testing the hypothesis that the covariance matrix ∑ is an identity matrix, by providing an unbiased estimator of tr [∑2] under the general model which requires no more computing time than the one available in the literature for normal model. In the two-sample case, tests for the equality of two covariance matrices are given. The asymptotic distributions of proposed tests in one-sample case are derived under the assumption that the sample size N = O(pδ), 1/2 < δ < 1, where p is the dimension of the random vector, and O(pδ) means that N/p goes to zero as N and p go to infinity. Similar assumptions are made in the two-sample case. |