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Title: Test for covariance structure for high-dimensional data under non-normality Authors:  Takahiro Nishiyama - Senshu University (Japan) [presenting]
Yuki Yamada - Tokyo University of Science (Japan)
Masashi Hyodo - Osaka Prefecture University (Japan)
Abstract: A test is proposed for making an inference about the block-diagonal covariance structure of a covariance matrix in non-normal high-dimensional data. Since the classical hypothesis testing methods based on the likelihood ratio degenerate when the dimensionality exceeds the sample size, we instead turn to a distance function between the null and alternative hypothesis. We prove that the limiting null distribution of the proposed test is normal under mild conditions when its dimension is substantially larger than its sample size. We further study the local power of the proposed test. Finally, we study the finite sample performance of the proposed test via Monte Carlo simulations. We demonstrate the relevance and benefits of the proposed approach for a number of alternative covariance structures.