Sphericity Test for High Dimensional Data Based on Random Matrix Theory
YUAN Shoucheng; ZHOU Jie; SHEN Jieqiong
College of Mathematics, Sichuan University, Chendu, 610064, China; College of Mathematics and Statistical Science, Puer University, Puer, 665000, China; School of Computer and Data Engineering, Zhejiang University Ningbo Institute of Technology, Ningbo, 315100, China
In this article we study test of sphericity for high-dimensional covariance matrix in the general population based on random matrix theory. When the sample size is less than data dimension, the classical likelihood ratio test has poor performance for test of sphericity. Thus, we propose a new statistic for test of sphericity by
using the higher moments of spectral distribution of the sample covariance matrix, and derive the asymptotic distribution of the statistic under the null hypothesis. Simulation results show that the proposed statistics can effectively improve the power of the test of sphericity for high dimensional data, and have especially significant effects for Spiked model, on the basis of controlling the type-one error probability.
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YUAN Shoucheng; ZHOU Jie; SHEN Jieqiong. Sphericity Test for High Dimensional Data Based on Random Matrix Theory. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2020, 36(4): 355-364.