${\sqrt{n}}$-uniformly consistent density estimation in nonparametric regression models | David Jacho-Chavez

# ${\sqrt{n}}$-uniformly consistent density estimation in nonparametric regression models

### Abstract

The paper introduces a ${\sqrt{n}}$-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.

Publication
Journal of Econometrics, (167), 2, pp. 305-316