Testing symmetry of unknown densities via smoothing with the generalized gamma kernels - Masayuki Hirukawa; Mari Sakudo (Econometrics, 2016)
This paper improves a kernel-smoothed test of symmetry through combining it with a new class of asymmetric kernels called the generalized gamma kernels. It is demonstrated that the improved test statistic has a normal limit under the null of symmetry and is consistent under the alternative. A test-oriented smoothing parameter selection method is also proposed to implement the test. Monte Carlo simulations indicate superior finite-sample performance of the test statistic. It is worth emphasizing that the performance is grounded on the first-order normal limit and a small number of observations, despite a nonparametric convergence rate and a sample-splitting procedure of the test.
Keywords: C12; C14; 330; asymmetric kernel; degenerate U-statistic; generalized gamma kernels; nonparametric kernel testing; smoothing parameter selection; symmetry test; two-sample goodness-of-fit test