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An Alternative Estimator for the Censored Quantile Regression Model

Moshe Buchinsky
Jinyong Hahn

Abstract

The paper introduces an alternative estimator for the linear censored quantile regression model. The objective function is globally convex and the estimator is a solution to a linear programming problem. Hence, a global minimizer is obtained in a finite number of simplex iterations. The suggested estimator also applies to the case where the censoring point is an unknown function of a set of regressors. It is shown that, under fairly weak conditions, the estimator has a $\sqrt${n}-convergence rate and is asymptotically normal. In the case of a fixed censoring point, its asymptotic property is nearly equivalent to that of 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.