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A consistent test of conditional parametric distributions. (English) Zbl 0967.62032
Summary: This paper proposes a new nonparametric test for conditional parametric distribution functions based on the first-order linear expansion of the Kullback-Leibler information function and the kernel estimation of the underlying distributions. The test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric distribution is correctly specified, whereas asymptotically rejecting the null with probability one if the parametric distribution is misspecified. The test is also shown to have power against any local alternatives approaching the null at rates slower than the parametric rate $$n^{1/2}$$. The finite sample performance of the test is evaluated via a Monte Carlo simulation.

##### MSC:
 62G10 Nonparametric hypothesis testing 62F03 Parametric hypothesis testing 62E20 Asymptotic distribution theory in statistics 65C05 Monte Carlo methods
##### Keywords:
Kullback-Leibler information; kernel estimation; simulation
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