Testing the Goodness of Fit of a Parametric Density Function by Kernel Method

Yanqin Fan

Econometric Theory, 1994, vol. 10, issue 02, pages 316-356

Abstract: Let F denote a distribution function defined on the probability space ( , 1 vector , ) for some ) and the quasimaximum likelihood estimate of f0( ) denoted by In and (ii) the integrated squared difference between a kernel estimate of f( , ) determines the form of the test statistic based on In. For each test developed, we also examine its asymptotic properties including consistency and the local power property. In particular, we show that tests developed in this paper, except the first one, are more powerful than the Kolmogorov-Smirnov test under the sequence of local alternatives introduced in Rosenblatt [12], although they are less powerful than the Kolmogorov-Smirnov test under the sequence of Pitman alternatives. A small simulation study is carried out to examine the finite sample performance of one of these tests.

Date: 1994
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