Antoniadis, Anestis, Fryzlewicz, Piotr 
ORCID: 0000-0002-9676-902X and Letué, Frédérique
(2010)
The Dantzig selector in Cox's proportional hazards model.
Scandinavian Journal of Statistics, 37 (4).
pp. 531-552.
ISSN 0303-6898
Abstract
The Dantzig selector (DS) is a recent approach of estimation in high-dimensional linear regression models with a large number of explanatory variables and a relatively small number of observations. As in the least absolute shrinkage and selection operator (LASSO), this approach sets certain regression coefficients exactly to zero, thus performing variable selection. However, such a framework, contrary to the LASSO, has never been used in regression models for survival data with censoring. A key motivation of this article is to study the estimation problem for Cox's proportional hazards (PH) function regression models using a framework that extends the theory, the computational advantages and the optimal asymptotic rate properties of the DS to the class of Cox's PH under appropriate sparsity scenarios. We perform a detailed simulation study to compare our approach with other methods and illustrate it on a well-known microarray gene expression data set for predicting survival from gene expressions.
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