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Econometrics 2016, 4(2), 28; doi:10.3390/econometrics4020028

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

1
Faculty of Economics, Setsunan University, 17-8 Ikeda Nakamachi, Neyagawa, Osaka 572-8508, Japan
2
Research Institute of Capital Formation, Development Bank of Japan, 9-7, Otemachi 1-chome, Chiyoda-ku, Tokyo 100-8178, Japan
3
Waseda Institute of Political Economy, Waseda University, 6-1 Nishiwaseda 1-chome, Shinjuku-ku, Tokyo 169-8050, Japan
4
Japan Economic Research Institute, 2-1, Otemachi 2-chome, Chiyoda-ku, Tokyo 100-0004, Japan
*
Author to whom correspondence should be addressed.
Academic Editor: Kerry Patterson
Received: 29 December 2015 / Revised: 10 May 2016 / Accepted: 30 May 2016 / Published: 17 June 2016
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Abstract

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. View Full-Text
Keywords: asymmetric kernel; degenerate U-statistic; generalized gamma kernels; nonparametric kernel testing; smoothing parameter selection; symmetry test; two-sample goodness-of-fit test asymmetric kernel; degenerate U-statistic; generalized gamma kernels; nonparametric kernel testing; smoothing parameter selection; symmetry test; two-sample goodness-of-fit test
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hirukawa, M.; Sakudo, M. Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels. Econometrics 2016, 4, 28.

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