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 ).
Lewbel, Arthur and Linton, Oliver B., "Nonparametric Censored Regression" (1998). Cowles Foundation Discussion Papers. 1434.