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Bandwidth Selection in Nonparametric Kernel Testing

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Author Info

  • Jiti Gao

    ()
    (School of Economics, University of Adelaide)

  • Irene Gijbels

    ()
    (Department of Mathematics, University of Leuven)

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Abstract

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.

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File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2009-01.pdf
File Function: First version, 2009
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Bibliographic Info

Paper provided by University of Adelaide, School of Economics in its series School of Economics Working Papers with number 2009-01.

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Length: 53 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:adl:wpaper:2009-01

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Related research

Keywords: choice of bandwidth parameter; Edgeworth expansion; nonparametric kernel testing; power function; size function;

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