Abstract

This article analyzes whether some existing tests for the p x p covariance matrix Sigma of the N independent identically distributed observation vectors work under non-normality. We focus on three hypotheses testing problems: (1) testing for sphericity, that is, the covariance matrix Sigma is proportional to an identity matrix I(p); (2) the covariance matrix Sigma is an identity matrix I(p); and (3) the covariance matrix is a diagonal matrix. It is shown that the tests proposed by Srivastava (2005) for the above three problems are robust under the non-normality assumption made in this article irrespective of whether N <= p or N >= p, but (N, p) -> infinity, and N/p may go to zero or infinity. Results are asymptotic and it may be noted that they may not hold for finite (N, p). (C) 2011 Published by Elsevier Inc.

Published in

Journal of Multivariate Analysis
2011, Volume: 102, number: 6, pages: 1090-1103
Publisher: ELSEVIER INC

SLU Authors

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Probability Theory and Statistics


Publication identifier

DOI: https://doi.org/10.1016/j.jmva.2011.03.003

Permanent link to this page (URI)

https://res.slu.se/id/publ/46803