The Dantzig selector in Cox's proportional hazards model

Anestis Antoniadis, Piotr Fryzlewicz and Frédérique Letué

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Dantzig selector; generalized linear models; LASSO; penalized partial likelihood; proportional hazards model; variable selection (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2010-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Published in Scandinavian Journal of Statistics, December, 2010, 37(4), pp. 531-552. ISSN: 0303-6898

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