<i>l</i>₁-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 paper considers estimation and model selection for a high-dimensional censored linear regression model. We combine <i>l</i>₁-penalization method with the ideas of Honoré and Powell (1994) and propose an <i>l</i>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 l1-penalized estimator, and find that the post-penalized estimator generally can perform better than the <i>l</i>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.