Kybernetika 54 no. 5, 908-920, 2018

A homogeneity test of large dimensional covariance matrices under non-normality

M. Rauf AhmadDOI: 10.14736/kyb-2018-5-0908


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.


high-dimensional inference, covariance testing, $U$-statistics, non-normality




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