2019/10/29 by Song Xi Chen, Bin Guo, Chen, Song Xi +3
Computer Science · Mathematics · #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Random Matrices and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1910.13074
openalex publication_date 2019/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider testing the equality of two high-dimensional covariance matrices by carrying out a multi-level thresholding procedure, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. We propose a multi-thresholding test that is shown to be powerful in detecting sparse and weak differences between two covariance matrices. The test is shown to have attractive detection boundary and to attain the optimal minimax rate in the signal strength under different regimes of high dimensionality and the sparsity of the signal. Simulation studies are conducted to demonstrate the utility of the proposed test.