Error distribution estimation in nonparametric regression with right censored selection biased data

In this presentation, we study the nonparametric regression model Y = m(X) +sigma(X) * epsilon where the error epsilon, with unknown distribution, is independent of the covariate X, and m(X) = E[Y|X] and sigma²(X) =Var[Y|X] are unknown smooth functions. The problem is to estimate the cumulative distribution function of the error in a nonparametric way when the
couple (X;Y) is subject to generalized bias selection while the positive response Y can be
right-censored. We propose a new estimator for the error distribution function. Asymptotic
properties of the proposed estimator are established, namely the rate of convergence and the
limiting distribution. A bootstrap procedure is developed to solve the critical problem of
the smoothing parameter choice. The performance of the proposed estimator is investigated
through simulations. Finally, a data set based on the mortality of diabetics is analyzed.