Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable

This paper presents a method for estimating the model A(Y)= min(beta'x + U, C), where Y is a scalar, ii is an unknown increasing function, X is a vector of explanatory variables, a is a vector of unknown parameters, U has unknown cumulative distribution function F, and C is a censoring threshold. It is not assumed that A and F belong to known parametric families; they are estimated nonparametrically. This model includes many widely used models as special cases, including the proportional hazards model with unobserved heterogeneity. The paper develops n(1/2)-consistent, asymptotically normal estimators of A and F. Estimators of beta that are n(1/2)-consistent and asymptotically normal already exist. The results of Monte Carlo experiments illustrate the finite-sample behavior of the estimators. (C) 1999 Elsevier Science S.A. All rights reserved. JEL classification: C14; C24; C41.