Simple resampling methods for censored regression quantiles

Powell (Journal of Econometrics 25 (1984) 303–325; Journal of Econometrics 32 (1986) 143–155) considered censored regression quantile estimators. The asymptotic covariance matrices of his estimators depend on the error densities and are therefore difficult to estimate reliably. The difficulty may be avoided by applying the bootstrap method (Hahn, Econometric Theory 11 (1995) 105–121). Calculation of the estimators, however, requires solving a nonsmooth and nonconvex minimization problem, resulting in high computational costs in implementing the bootstrap. We propose in this paper computationally simple resampling methods by convexfying Powellʹs approach in the resampling stage. A major advantage of the new methods is that they can be implemented by efficient linear programming. Simulation studies show that the methods are reliable even with moderate sample sizes.