Nonparametric Censored and Truncated Regression

The nonparametric censored regression model, with a fixed, known censoring point (normalized to zero), is y=max[0,m(x)+e], where both the regression function m(x) and the distribution of the error e are unknown. This paper provides consistent estimators of m(x) and its derivatives with respect to each element of x. The convergence rate is the same as for an uncensored nonparametric regression and its derivatives. We also provide root n estimates of weighted average derivatives of m(x), which equal the coefficients in linear or partly linear specifications for m(x). Some estimators already exist for randomly censored nonparametric models, but we provide estimators for fixed censoring, and for truncated regression. The estimators are based on the relationship that the derivative of E(y|x) with respect to m(x) equals E[I(y>0)|x]. We derive A similar expression involving higher moments of y also, which is required for the truncated regression model. An advantage of our estimator is that, unlike quantile methods, no a priori information is required regarding the degree of censoring at each x. Also error symmetry is not assumed. Another advantage is that our estimator extends to nonparametric truncated regression, so m(x) and its derivates can be estimated when only observations having m(x) + e > 0 are observed. We also provide an extension that permits estimation in the presence of a general form of heteroscedasticity.(This abstract was borrowed from another version of this item.)