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A note on testing the covariance matrix for large dimension

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  • Birke, Melanie
  • Dette, Holger

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 = ∞.

Suggested Citation

  • Birke, Melanie & Dette, Holger, 2003. "A note on testing the covariance matrix for large dimension," Technical Reports 2004,02, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200402
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    References listed on IDEAS

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    1. Jonsson, Dag, 1982. "Some limit theorems for the eigenvalues of a sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 1-38, March.
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