Some Hypothesis Tests for the Covariance Matrix When the Dimension Is Large Compared to the Sample Size

@inproceedings{Wolf2001SomeHT,
title={Some Hypothesis Tests for the Covariance Matrix When the Dimension Is Large Compared to the Sample Size},
author={Michael Wolf},
year={2001}
}

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… CONTINUE READING

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