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A1017
Title: Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding Authors:  Bin Guo - Southwestern University of Finance and Economics (China) [presenting]
Abstract: Testing and signal identification is considered for covariance matrices from two populations. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, 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. It is shown that the proposed test is more powerful than the existing tests in detecting sparse and weak signals in covariances. Multiple testing procedures are constructed to discover different covariances and the sub-groups of variables with different covariance structures between the two populations. The proposed procedures are based on the multi-level thresholding test, which is able to control the false discovery proportion (FDP) with high power. Simulation experiments and a case study on the returns of the SP500 stocks before and after the COVID-19 pandemic are conducted to demonstrate and compare the utilities of the proposed methods.