A consistent test of conditional parametric distributions. (English) Zbl 0967.62032

Zheng, John Xu

Econom. Theory 16, No. 5, 667-691 (2000).

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