A consistent test of conditional parametric distributions

This paper proposes a new nonparametric test for conditional parametric dis tribution functions based on the first-order linear expansion of the Kullba ck-Leibler information function and the kernel estimation of the underlying distributions. The test statistic is shown to be asymptotically distribute d standard normal under the null hypothesis that the parametric distributio n is correctly specified, whereas asymptotically rejecting the null with pr obability one if the parametric distribution is misspecified. The test is a lso shown to have power against any local alternatives approaching the null at rates slower than the parametric rate n(-1/2). The finite sample perfor mance of the test is evaluated via a Monte Carlo simulation.