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| 摘要: |
| 本文讨论了条件分布对称性检验的问题. 借助 energy distance 的概念与思路，提出了conditaional energy distance的概念，基于conditaional energy distance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-统计量理论证明了该检验统计量的一致性及在原假设下的渐近正态性 |
| 关键词: 条件分布对称性 energy distance 随机核U-统计量 一致性 渐近正态性 |
| DOI： |
| 分类号:O212.7 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| A Consistent Test for Conditional Symmetry and Its Asymptotically Normality |
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Chen Minqiong
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| Abstract: |
| We propose a new test of conditional symmetry based on the concept of conditional energy distance. The test statistic
has the form of a $U$-statistic with random kernel. It is shown to be asymptotically normal under the null hypothesis of conditional symmetry and consistent against any conditional asymmetric distributions |
| Key words: Conditional symmetry test Conditional energy distance U-statistic with random kernel Consistent Asymptotically normality |
