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

by 1,* and 2,3,4
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
Econometrics 2016, 4(2), 28; https://doi.org/10.3390/econometrics4020028
Received: 29 December 2015 / Revised: 10 May 2016 / Accepted: 30 May 2016 / Published: 17 June 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. 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
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MDPI and ACS Style

Hirukawa, M.; Sakudo, M. Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels. Econometrics 2016, 4, 28. https://doi.org/10.3390/econometrics4020028

AMA Style

Hirukawa M, Sakudo M. Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels. Econometrics. 2016; 4(2):28. https://doi.org/10.3390/econometrics4020028

Chicago/Turabian Style

Hirukawa, Masayuki, and Mari Sakudo. 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels" Econometrics 4, no. 2: 28. https://doi.org/10.3390/econometrics4020028

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