Cox's proportional hazards model with a high-dimensional and sparse regression parameter

TL;DR

This paper extends Cox's proportional hazards model to high-dimensional, sparse data using the Dantzig selector, proving variable selection consistency and enabling asymptotically normal estimators for key parameters.

Contribution

It introduces the use of the Dantzig selector in high-dimensional Cox models and proves its variable selection consistency.

Findings

Proves variable selection consistency of the Dantzig selector in this setting

Constructs asymptotically normal estimators for the regression parameter

Reduces model dimension effectively in high-dimensional sparse data

Abstract

This paper deals with the proportional hazards model proposed by D. R. Cox in a high-dimensional and sparse setting for a regression parameter. To estimate the regression parameter, the Dantzig selector is applied. The variable selection consistency of the Dantzig selector for the model will be proved. This property enables us to reduce the dimension of the parameter and to construct asymptotically normal estimators for the regression parameter and the cumulative baseline hazard function.