√n-uniformly consistent density estimation in nonparametric regression models

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. The results derived in the paper adapt general U-processes theory to the inclusion of infinite dimensional nuisance parameters. (C) 2011 Elsevier B.V. All rights reserved.