Nonparametric Censored Regression

The nonparametric censored regression model is y = max[c, m(x) + e], where both the regression function m(x) and the distribution of the error e are unknown, but the fixed censoring point c is known. This paper provides a simple consistent estimator of the derivative of m(x) with respect to each element of x. The convergence rate of this estimator is the same as for the derivatives of an uncensored nonparametric regression. We then estimate the regression function itself by solving the associated partial differential equation system. We show that our estimator of m(x) achieves the same rate of convergence as the usual estimators in uncensored nonparametric regression. We also provide root n estimates of weighted average derivatives of m(x), which equal the coefficients in any linear or partly linear specification for m(x).