A consistent test for conditional symmetry and its asymptotical normality. (English) Zbl 1438.62088
Summary: In this paper, we investigate the problem of testing the conditional symmetry of a random vector and give 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.
MSC:
62G10 | Nonparametric hypothesis testing |
62G20 | Asymptotic properties of nonparametric inference |
62G30 | Order statistics; empirical distribution functions |