基于特征函数的条件分布对称性的一致性检验
A Consistent Test for Conditional Symmetry Based on Characteristic Function
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摘要: 本文讨论了一个随机向量在给定另一随机向量下的条件分布关于0对称的检验问题. 从相关的两个联合分布的经验特征函数之差的模出发,通过选取适当的权重函数对模进行积分后, 我们得到了一个简单的检验统计量,该检验统计量具有V-,统计量形式, 利用V-,统计量理论,我们证明了该检验统计量的渐近性质,包括估计的一致性及在原假设下和备择假设下的渐近分布.数值模拟显示我们的检验方法受条件向量维数的影响很小, 并且不需要矩的假设.最后我们通过一个简单的实例分析来说明本文方法的具体应用.Abstract: This article proposes a new consistent nonparametric test of the hypothesis that a random vector is symmetrically distributed given another random vector. The test is based on the weighted integral of the discrepancy between two empirical characteristic functions. By choosing a special weighted function, we obtain a simple form of the test statistic, which is the form of a V-\,statistic. Using the theory of V-\,statistic, we derive the asymptotical properties of the test. Simulation results show that our test is slightly affected by the dimension of the conditional vector and often still possess high power when the conditional vector has no finite moments. We also illustrate the power effectiveness of our test in the analysis of a real dataset.