Tests for Covariance Matrices in High Dimension with Less Sample Size

Muni S. Srivastava, Hirokazu Yanagihara and Tatsuya Kubokawa
Additional contact information
Muni S. Srivastava: Department of Statistics, University of Toronto
Hirokazu Yanagihara: Department of Mathematics, Hiroshima University
Tatsuya Kubokawa: Faculty of Economics, The University of Tokyo

No CIRJE-F-933, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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 ( p δ ), 1/2 < δ < 1, where p is the dimension of the random vector, and O ( p δ ) means that N/p goes to zero as N and p go to infinity. Similar assumptions are made in the two-sample case.

Pages: 25 pages
Date: 2014-06
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (25)

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