-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 l1-penalization method with the ideas of pairwise difference and propose an l1-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 l1-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.

高维数据（high-dimensional data）如今在实证经济学各领域中已十分易得且愈发普遍。本文针对高维截尾线性回归模型，研究其估计与模型选择问题。我们将L1惩罚方法与成对差分思想相结合，提出了一种L1惩罚成对差分最小绝对偏差（least absolute deviations，LAD）估计量。在正则性条件下，我们证明了该估计量的估计一致性与模型选择一致性。我们还提出了一种后惩罚估计量：将无惩罚成对差分LAD估计应用于由L1惩罚估计量所选择的模型，结果表明，后惩罚估计量在收敛速度层面通常优于L1惩罚估计量。我们基于交替方向乘子法（alternating direction method of multipliers），提出了用于计算所提估计量的新型快速算法。我们开展了一项模拟研究，用以验证所提算法在计算时长上的显著优化，并展示所提估计量令人满意的统计性能。