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| 引用本文： | ����,�����,������,�����.���ھ���ֲ������ĸ�ά��̬�Լ���[J].应用概率统计,2020,36(1):41-58. |
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| 作者姓名： | ���� ����� ������ ����� |
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| 作者单位： | ?й????????????, ????, 100872;???????????????, ????, 100871;?й???????????????????????, ????, 100872 |
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| 摘 要： |
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| 关 键 词： | ??? ???????? EDF????????? |
Empirical Distribution Function Based Statistics for Testing High Dimensional Normality |
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| CUI Jiarong,ZHU Fengyi,LIU Jiamin,XU Wangli.Empirical Distribution Function Based Statistics for Testing High Dimensional Normality[J].Chinese Journal of Applied Probability and Statisties,2020,36(1):41-58. |
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| Authors: | CUI Jiarong ZHU Fengyi LIU Jiamin XU Wangli |
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| Institution: | 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 |
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| Abstract: | ??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. |
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