Root-n Uniformly Consistent Density Estimation in Nonparametric Regression Models

Abstract

The paper introduces a root-n consistent estimator of the probability density function of the response variable in a nonparametric regression model. The proposed estimator is shown to have a (uniform) asymptotic normal distribution, and it is computationally very simple to calculate. A Monte Carlo experiment confirms our theoretical results, and an empirical application demonstrates its usefulness. The results derived in the paper adapts general U-processes theory to the inclusion of infinite dimensional nuisance parameters.