Abstract
Tests for certain covariance structures, including sphericity, are presented when the data may be high-dimensional but not necessarily normal. The tests are formulated as functions of location-invariant estimators defined as U-statistics of higher order kernels. Under a few mild assumptions, the limit distributions of the tests are shown to be normal. The accuracy of the tests is demonstrated by simulations.
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Ahmad, M.R. On testing sphericity and identity of a covariance matrix with large dimensions. Math. Meth. Stat. 25, 121–132 (2016). https://doi.org/10.3103/S1066530716020034
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DOI: https://doi.org/10.3103/S1066530716020034