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

TL;DR

This paper establishes the $l_q$ consistency of the Dantzig selector in high-dimensional Cox proportional hazards models, under weaker matrix conditions than previous studies.

Contribution

It introduces new theoretical results proving $l_q$ consistency of the Dantzig selector with weaker assumptions on the Hessian matrix approximation.

Findings

Proves $l_q$ consistency for all $q \, \geq \, 1$

Uses weaker matrix conditions than prior research

Applies to high-dimensional sparse Cox models

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 $q \geq 1$ 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.