The l_q consistency of the Dantzig Selector for Cox's Proportional Hazards Model

2016/05/13 by Kou Fujimori, Fujimori, Kou, Yoichi Nishiyama +1
Mathematics · #62N02 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:62N02 #stat.TH

paper · pdf · doi:10.48550/arxiv.1605.04059

13 pages

arxiv created 2016/05/13 · arxiv updated 2016/05/16

Abstract

The Dantzig selector for the proportional hazards model proposed by D.R. Cox is studied in a high-dimensional and sparse setting. We prove the l_q consistency for all q ≥ 1 of some estimators based on the compatibility factor, the weak cone invertibility factor, and the restricted eigenvalue for certain deterministic matrix which approximates the Hessian matrix of log partial likelihood. Our matrix conditions for these three factors are weaker than those of previous researches.

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