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Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters

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Author Info
Fan, Yanqin
Abstract

In this paper, we study the bias-corrected test developed in Fan (1994). It is based on the integrated squared difference between a kernel estimator of the unknown density function of a random vector and a kernel smoothed estimator of the parametric density function to be tested under the null hypothesis. We provide an alternative asymptotic approximation of the finite-sample distribution of this test by fixing the smoothing parameter. In contrast to the normal approximation obtained in Fan (1994) in which the smoothing parameter shrinks to zero as the sample size grows to infinity, we obtain a non-normal asymptotic distribution for the bias-corrected test. A parametric bootstrap procedure is proposed to approximate the critical values of this test. We show both analytically and by simulation that the proposed bootstrap procedure works. Consistency and local power properties of the bias-corrected test with a fixed smoothing parameter are also discussed.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 14 (1998)
Issue (Month): 05 (October)
Pages: 604-621
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Handle: RePEc:cup:etheor:v:14:y:1998:i:05:p:604-621_14

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  1. Qi Li & Esfandiar Maasoumi & Jeffrey S. Racine, 2008. "A Nonparametric Test For Equality Of Distributions With Mixed Categorical And Continuous Data," Emory Economics 0805, Department of Economics, Emory University (Atlanta). [Downloadable!]
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