Computational study of the error distribution in right-censored and selection-biased regression models

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.