l1-Penalized Pairwise Difference Estimation for a High-Dimensional Censored Regression Model

High-dimensional data are nowadays readily available and increasingly common in various fields of empirical economics. This article considers estimation and model selection for a high-dimensional censored linear regression model. We combine l(1)-penalization method with the ideas of pairwise difference and propose an l(1)-penalized pairwise difference least absolute deviations (LAD) estimator. Estimation consistency and model selection consistency of the estimator are established under regularity conditions. We also propose a post-penalized estimator that applies unpenalized pairwise difference LAD estimation to the model selected by the l(1)-penalized estimator, and find that the post-penalized estimator generally can perform better than the l(1)-penalized estimator in terms of the rate of convergence. Novel fast algorithms for computing the proposed estimators are provided based on the alternating directionmethod of multipliers. A simulation study is conducted to showthe great improvements of our algorithms in terms of computation time and to illustrate the satisfactory statistical performance of our estimators.