Simple resampling methods of approximating the distribution of LAD estimators for doubly censored regression models

Recently, least absolute deviation (LAD) estimator for median regression models with doubly censored data was proposed and the asymptotic normality of the estimator was established, and the methods based on bootstrap and random weighting were proposed respectively to approximate the distribution of the LAD estimators. But the calculation of the estimators requires solving a non-convex and non-smooth minimization problem, resulting in high computational costs in implementing the bootstrap or random weighting method directly. In this paper, computationally simple resampling methods are proposed to approximate the distribution of the doubly censored LAD estimators. The objective functions in the resampling stage of the new methods are piece-wise linear and convex, and their minimizer can be obtained by the linear programming in the same way as that for the case of uncensored median regression.