Optimal modification of the LRT for the equality of two high-dimensional covariance matrices

2017/06/21 by Qiuyan Zhang, Jiang Hu, Zhang, Qiuyan +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Random Matrices and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1706.06774

openalex publication_date 2017/06/21 · openalex created_date 2017/06/30 · openalex updated_date 2026/07/28

Abstract

This paper considers the optimal modification of the likelihood ratio test (LRT) for the equality of two high-dimensional covariance matrices. The classical LRT is not well defined when the dimensions are larger than or equal to one of the sample sizes. In this paper, an optimally modified test that works well in cases where the dimensions may be larger than the sample sizes is proposed. In addition, the test is established under the weakest conditions on the moments and the dimensions of the samples. We also present weakly consistent estimators of the fourth moments, which are necessary for the proposed test, when they are not equal to 3. From the simulation results and real data analysis, we find that the performances of the proposed statistics are robust against affine transformations.

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