A Consistent Test for Conditional Symmetry Based on Characteristic Function

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.