Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

Olivier Ledoit and Michael Wolf

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

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 non-zero 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.

Keywords: Concentration asymptotics; equality test; sphericity test (search for similar items in EconPapers)
JEL-codes: C12 C52 (search for similar items in EconPapers)
Date: 2001-10
New Economics Papers: this item is included in nep-ecm, nep-ent, nep-ets and nep-net
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:575

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