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

Consider the regression model Y = m(X) + σ(X) Ɛ , where m(X) = E[Y|X] and σ²(X) = Var[Y|X] are unknown smooth functions and the error Ɛ (with unknown distribution) is independent of X. The pair (X;Y) is subject to generalized selection bias and the response to right censoring. We construct a new estimator for the cumulative distribution function of the error Ɛ , 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.