JOURNAL OF THE JAPAN STATISTICAL SOCIETY
Online ISSN : 1348-6365
Print ISSN : 1882-2754
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Some Tests Concerning the Covariance Matrix in High Dimensional Data
Muni S. Srivastava
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2005 Volume 35 Issue 2 Pages 251-272

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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 pof the data. Under the condition that (tr Σip) 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.

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© 2005 Japan Statistical Society
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