Some Large Deviations Limit Theorems in Conditional Nonparametric Statistics

Abstract

We establish pointwise and uniform large deviations limit theorems of Chernoff-type for the conditional empirical process. On the other hand, we state the pointwise large deviations theorem for the Nadaraya-Watson estimator of the regression function. The estimations are based on sequences of independent and identically distributed random vectors. We derive then some implications of our results in the study of asymptotic efficiency of goodness-of-fit test based on uniform deviation of the conditional empirical distribution function with respect to its theoretical distribution. Moreover, we deduce the inaccuracy rate in conditional distribution functions estimation.