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英文文献：Bandwidth Selection in Nonparametric Kernel Testing-非参数核检验中的带宽选择
英文文献作者：Jiti Gao,Irene Gijbels
英文文献摘要：
We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed?–form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions. For example, when a significance level is given, we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level. Both asymptotic theory and methodology are established. In addition, we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example.
提出了一种非参数核检验中带宽选择的有效方法。主要思想是找到有关检验的渐近分布的埃奇沃思展开。由于内核带宽的参与在埃奇沃思扩张的主要术语,我们能够建立closedA-form表达式来显式地表示大小和幂函数的主要条款,然后确定带宽应该按照一定的要求选择大小和幂函数。例如，在给定显著性水平时，我们可以选择带宽，使幂函数最大，而大小函数由显著性水平控制。建立了渐近理论和方法。此外，我们还为所建立的方法的实际实现开发了一个简单的实现程序，并通过两个仿真例子和一个实际数据例子加以说明。
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