A note on testing the covariance matrix for large dimension

Melanie Birke and Holger Dette

No 2004,02, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: We consider the problem of testing hypotheses regarding the covariance matrix of multivariate normal data, if the sample size s and dimension n satisfy lim [n,s→∞] n/s = y. Recently, several tests have been proposed in the case, where the sample size and dimension are of the same order, that is y ∈ (0,∞). In this paper we consider the cases y = 0 and y = ∞. It is demonstrated that standard techniques are not applicable to deal with these cases. A new technique is introduced, which is of its own interest, and is used to derive the asymptotic distribution of the test statistics in the extreme cases y = 0 and y = ∞.

Keywords: sphericity test; random matrices; Wishart distribution (search for similar items in EconPapers)
Date: 2003
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