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

Abstract

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 direction method of multipliers. A simulation study is conducted to show the great improvements of our algorithms in terms of computation time and to illustrate the satisfactory statistical performance of our estimators.