Empirical Distribution Function Based Statistics for Testing High Dimensional Normality
CUI Jiarong; ZHU Fengyi; LIU Jiamin; XU Wangli
School of Statistics, Renmin University of China, Beijing, 100872, China; School of Mathematical Sciences, Peking University, Beijing, 100871, China; Center for Applied Statistics and School of Statistics, Renmin University of China, Beijing, 100872, China
Kolmogorov-Smirnov (KS), Cramer-von Mises (CM) and Anderson-Darling (AD) test, which are based on empirical distribution function (EDF), are well-known statistics in testing univariate normality. In this paper, we focus on the high dimensional case and propose a family of generalized EDF based statistics to test the high-dimensional normal distribution by reducing the dimension of the variable. Not only can we approximate the corresponding critical values of three statistics by Monte Carlo method, we also can investigate the approximate distributions of proposed statistics based on approximate formulas in univariate case under null hypothesis. The Monte Carlo simulation is carried out to demonstrate that the performance of proposed statistics is more competitive than existing methods under some alternative hypotheses. Finally, the proposed tests are applied to real data to illustrate their utility.
The project was supported by the National Natural Science Foundation of China (Grant No: 11971478) and the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (Grant No: 16JJD910002).
CUI Jiarong,ZHU Fengyi,LIU Jiamin��. Empirical Distribution Function Based Statistics for Testing High Dimensional Normality[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2020, 36(1): 41-58.