The paper introduces an estimator for the linear censored quantile regression model when the censoring point is an unknown function of a set of regressors. The objective function minimized is convex and the minimization problem is a linear programming problem, for which there is a global minimum. The suggested procedure applies also to the special case of a ﬁxed known censoring point. Under fairly weak conditions the estimator is shown to have n -convergence rate and is asymptotically normal. In the special case of a ﬁxed censoring point it is asymptotically equivalent to the estimator suggested by Powell (1984, 1986a). A Monte Carlo study performed shows that the suggested estimator has very desirable small sample properties. It precisely corrects for the bias induced by censoring, even when there is a large amount of censoring, and for relatively small sample sizes. The estimator outperforms that suggested by Powell in cases where both apply.
Buchinsky, Moshe and Hahn, Jinyong, "Quantile Regression Model with Unknown Censoring Point" (1995). Cowles Foundation Discussion Papers. 1339.