Pairwise difference estimators of censored and truncated regression models

This paper proposes a class of estimators of the semiparametric censored regression model under the assumption that the error terms are i.i.d. and independent of the covariates. The estimators exploit the fact that, for a pair of observations, a particular transformation of the censored variables (depending upon the parameter vector and both covariate vectors) will be identically distributed. Therefore, the difference in the transformed dependent variables will be symmetrically distributed around zero when the transformation is evaluated at the true parameter vector. An analogous class of estimators for the truncated regression model includes the Bhattacharya, Chernoff, and Yang (1983) estimator as a special case. The estimators are defined as minimizers of U-processes, so the large-sample theory for classical M-estimators is extended to this case. Conditions are given to ensure root-n-consistency and asymptotic normality of the estimators, and a small-scale simulation study for the censored regression estimator suggest that it will be well-behaved in finite samples.