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. 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). An extension permits estimation in the presence of a general form of heteroskedasticity. We also extend the estimator to the nonparametric truncated regression model, in which only uncensored data points are observed.