Uniform law of the logarithm for the local linear estimator of the conditional distribution function

Abstract

In this Note, we first recall the results of the behaviour of the nonparametric estimator of the conditional distribution function which we can find in the literature. We establish exact rate of strong uniform consistency for the local linear estimator of the conditional distribution function. Our methods of proofs are based upon modern empirical process theory in the spirit of the results of Einmahl and Mason (2000) [5] and Deheuvels and Mason (2004) [3].