The Dantzig selector in Cox's proportional hazards model
Résumé
In this talk, we present several papers about variable selection by the team UJF of the IAP Network. Among them, we focus on an adaptation of the Dantzig Selector procedure in the Cox's proportional hazards framework. This procedure performs variable selection in high-dimensional linear regression models with a large number of explanatory variables and a relatively small number of observations, setting some regression coe cients to exactly zero. We study the theory, the computational advantages and the optimal asymptotic rate properties of the Danzig selector to the class of Cox's proportional hazards under appropriate sparsity scenarios. We perform a detailed simulation study to compare our approach to other possible methods and demonstrate it on some well-known microarray gene expression data sets for predicting survival from gene expressions.