Bandwidth Selection in Nonparametric Kernel Testing

Jiti Gao

doi:10.1198/016214508000000968

Bandwidth Selection in Nonparametric Kernel Testing

2012-01-01

103

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AI

DOI：10.1198/016214508000000968

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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 dire 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.

Keyword:

Choice of bandwidth parameter

Edgeworth expansion

Nonparametric kernel testing

Power function

Size function

Bandwidth Selection in Nonparametric Kernel Testing

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