条件分布对称性的一个一致性检验及渐近正态性（英文）  

A CONSISTENT TEST FOR CONDITIONAL SYMMETRY AND ITS ASYMPTOTICAL NORMALITY

作　　者：陈敏琼 CHEN Min-qiong(School of Economics and Trade,Xinhua College of Sun Yat-Sen University,Guangzhou 510520,China;School of Mathematics,Sun Yat-Sen University,Guangzhou 510275,China)

机构地区：[1]中山大学新华学院经济与贸易学院,广东广州510520 [2]中山大学数学学院,广东广州510275

出　　处：《数学杂志》2019年第2期159-170,共12页Journal of Mathematics

基　　金：Supported by Social Science Foundation of Guangdong Province for Young Innovative Talents(2016WQNCX189)

摘　　要：本文研究了条件分布对称性检验的问题.借助能量距离的概念与思路,提出了条件能量距离的概念.基于条件能量距离构造出一个新的条件分布对称性的检验统计量,该统计量具有带随机核的U-统计量的形式.利用带随机核U-统计量理论证明得到该检验统计量的一致性及在原假设下的渐近正态性的结果.In this paper,we investigate the problem of testing the conditional symmetry of a random vector given another random vector.We propose a new test based on the concept of conditional energy distance.The test statistic has the form of a U-statistic with random kernel.By using the theory of U-statistic,we prove that the test statistic is asymptotically normal under the null hypothesis of conditional symmetry and consistent against any conditional asymmetric distribution.

关 键 词：条件分布对称性 能量距离 随机核U-统计量 一致性 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]