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August 2002 Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size
Olivier Ledoit, Michael Wolf
Ann. Statist. 30(4): 1081-1102 (August 2002). DOI: 10.1214/aos/1031689018

Abstract

This paper analyzes whether standard covariance matrix tests work when dimensionality is large, and in particular larger than sample size. In the latter case, the singularity of the sample covariance matrix makes likelihood ratio tests degenerate, but other tests based on quadratic forms of sample covariance matrix eigenvalues remain well-defined. We study the consistency property and limiting distribution of these tests as dimensionality and sample size go to infinity together, with their ratio converging to a finite nonzero limit. We find that the existing test for sphericity is robust against high dimensionality, but not the test for equality of the covariance matrix to a given matrix. For the latter test, we develop a new correction to the existing test statistic that makes it robust against high dimensionality.

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Olivier Ledoit. Michael Wolf. "Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size." Ann. Statist. 30 (4) 1081 - 1102, August 2002. https://doi.org/10.1214/aos/1031689018

Information

Published: August 2002
First available in Project Euclid: 10 September 2002

zbMATH: 1029.62049
MathSciNet: MR1926169
Digital Object Identifier: 10.1214/aos/1031689018

Subjects:
Primary: 62H15
Secondary: 62E20

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 4 • August 2002
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