Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels
Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels
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DOI：
10.3390/econometrics4020028
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发表时间：
2016-06
期刊：
影响因子：
1.5
通讯作者：
Masayuki Hirukawa;Mari Sakudo
中科院分区：
文献类型：
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作者：
Masayuki Hirukawa;Mari Sakudo
本文通过将核平滑对称性测试与一类新的非对称核（称为广义伽马核）相结合，改进了核平滑对称性测试。结果表明，改进的检验统计量在零对称性下具有正常极限，并且在替代方案下保持一致。还提出了一种面向测试的平滑参数选择方法来实现测试。蒙特卡罗模拟表明检验统计量具有优异的有限样本性能。值得强调的是，尽管测试具有非参数收敛速度和样本分割程序，但性能仍基于一阶正常极限和少量观测。
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.