On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution  

作　　者：JING Ping 1 and ZHU Lixing 2 1. Mathematics Lab, China University of Mining & Technology, Beijing 100083, China 2. Probability Lab, Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China 

出　　处：《Chinese Science Bulletin》1998年第6期450-458,共9页

摘　　要：Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关 键 词：BOOTSTRAP approximation PROJECTION PURSUIT type statistic ELLIPTICAL symmetry. 

分 类 号：O213[理学—概率论与数理统计]