Fast Restoration Dantzig Selection for Censored Data

Dimension reduction, modeland variable selectionhavebecome ubiquitous concepts in modern statisticalscience. Thispaperis concernedwith simultaneous estimation and variable selectionin thelinear model orleast-squares setup,principlebuildingblocks of complete-data model selection techniques. In contrast to the complete-data setup, we considerthecommonsituationwheretheoutcomesmayberight-censored. Threemost common estimatorsin this settinginclude the rank-based estimator, theBuckley-James estimator, andinverse-probability weighted(IPW) estimator. TheBuckley-James and IPW estimators are popular among applied statisticians because the estimators are based on simple missing data principles and they require no knowledge of linear programming. However, both estimators suffer difficulties. The IPW estimator is particularly inefficient whiletheBuckley-James estimating functionpossesses multiple roots in large and small samples and its iterative estimation procedure may result in infinite oscillation. Recently, authors have rediscovered that infinite oscillation can be avoided with consistent initial value. The goal of this paper is to offer a new Buckley-Jamestype estimator for high dimensional, sparse regression in the accelerated failure time model. Theideaisto start with agoodinitial value and replacelinear regression with Dantzig selection (DS). Compared with competing DS-type estimators for censored survival data, our method is much faster because it performs the DS optimization once, not iteratively. We illustrate the utility of this method through simulation studies and application to three real data sets.