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Title:A note on testing the covariance matrix for large dimension PDF Logo
Authors:Birke, Melanie
Dette, Holger
Issue Date:2003
Series/Report no.:Technical Report // Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2004,02
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 = ∞.
Subjects:sphericity test
random matrices
Wishart distribution
Document Type:Working Paper
Appears in Collections:Technical Reports, SFB 475: Komplexitätsreduktion in multivariaten Datenstrukturen, TU Dortmund

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