Geodesic
A homogeneity test of large dimensional covariance matrices under non-normality
Kybernetika, Tome 54 (2018) no. 5, pp. 908-920.

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A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as $U$-statistics and the corresponding theory is exploited to derive the normal limit of the statistic under a few mild assumptions as both sample size and dimension grow large. Simulations are used to assess the accuracy of the statistic.
DOI : 10.14736/kyb-2018-5-0908
Classification : 62H15
Keywords: high-dimensional inference; covariance testing; $U$-statistics; non-normality 
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Ahmad, M. Rauf. A homogeneity test of large dimensional covariance matrices under non-normality. Kybernetika, Tome 54 (2018) no. 5, pp. 908-920. doi : 10.14736/kyb-2018-5-0908. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-5-0908/

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