J. Japan Statist. Soc., Vol. 35 (No. 2), pp. 251-272, 2005
Muni S. Srivastava
Abstract. In this paper, tests are developed for testing certain hypotheses on the covariance matrix Σ, when the sample size N = n + 1 is smaller than the dimension p of the data. Under the condition that (tr Σi/p) exists and > 0, as p → ∞, i = 1,...,8, tests are developed for testing the hypotheses that the covariance matrix in a normally distributed data is an identity matrix, a constant time the identity matrix (spherecity), and is a diagonal matrix. The asymptotic null and non-null distributions of these test statistics are given.
Key words and phrases: Asymptotic distributions, multivariate normal, null and non-null distributions, sample size smaller than the dimension.