The consistency of the Dantzig selector for Cox’s proportional hazards model

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• 作者：Kou Fujimori^a ; ^{wisteria_forest@toki.waseda.jp" class="auth_mail" title="E-mail the corresponding author} ; Yoichi Nishiyama^b ; ^{nishiyama@waseda.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Proportional hazards model ; Dantzig selector ; Consistency
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：181
• 期：Complete
• 页码：62-70
• 全文大小：412 K

文摘

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 ce4a" title="Click to view the MathML source">l_q$l_q$ consistency for all the MathML source">q∈[1,∞]$q\in [1,\infty ]$ 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 factors are weaker than those of previous researches.