A CONSISTENT TEST OF CONDITIONAL PARAMETRIC DISTRIBUTIONS

Abstract

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.