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

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.