Estimation of the error distribution in nonparametric regression with cross-sectional data

In this article, we study the nonparametric regression model Y=m(X)+varepsilon where m(x)=E[Y|X=x] and sigma²(x)=Var[varepsilon|X=x] are unknown smooth functions, and the error varepsilon has zero mean and finite variance conditionally on X=x. The problem consists in estimating the cumulative distribution function of the error in a nonparametric way when the couple (X,Y) is obtained by cross-sectional sampling while the positive response Y can be right-censored. We propose a new estimator for the error distribution function based on the estimators of m(.) and sigma²(.) described in Heuchenne and Laurent 2014. A bootstrap procedure is developed to solve the critical problem of the smoothing parameter choice. We assess the performance of the proposed estimator through simulations. Finally, a data set based on the mortality of diabetics is analyzed. (Heuchenne Cédric and Laurent Géraldine, Nonparametric regression with cross-sectional data: an alternative to conditional product-limit estimators, 2014)