Computational treatment of the error distribution in nonparametric regression with right-censored and selection-biased data

Abstract

Consider the regression model Y = m(X) + σ(X)ε, where m(X) = E[Y |X] and σ 2(X) = V ar[Y |X] are unknown smooth functions and the error ε (with unknown distribution) is independent of X. The pair (X, Y ) is subject to parametric selection bias and the response to right censoring. We construct a new estimator for the cumulative distribution function of the error ε, and develop a bootstrap technique to select the smoothing parameter involved in the procedure. The estimator is studied via extended simulations and applied to real unemployment data. © Springer-Verlag Berlin Heidelberg 2010.