Some tests for the covariance matrix with fewer observations than the dimension under non-normality

Muni S. Srivastava, Tõnu Kollo and Dietrich von Rosen

Journal of Multivariate Analysis, 2011, vol. 102, issue 6, 1090-1103

Abstract: This article analyzes whether some existing tests for the pxp 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 Ip; (2) the covariance matrix [Sigma] is an identity matrix Ip; 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, 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).

Date: 2011
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