Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels

Econometrics

Masayuki Hirukawa¹  Mari Sakudo² 

[1] Faculty of Economics, Setsunan University, 17-8 Ikeda Nakamachi, Neyagawa, Osaka 572-8508, Japan;Research Institute of Capital Formation, Development Bank of Japan, 9-7, Otemachi 1-chome, Chiyoda-ku, Tokyo 100-8178, Japan;

关键词: asymmetric kernel;    degenerate U-statistic;    generalized gamma kernels;    nonparametric kernel testing;    smoothing parameter selection;    symmetry test;    two-sample goodness-of-fit test;   

DOI  :  10.3390/econometrics4020028

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown