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Scandinavian Journal of Statistics doi: 10.1111/j.1467-9469.2009.00685.x
 

Summary: Scandinavian Journal of Statistics
doi: 10.1111/j.1467-9469.2009.00685.x
© 2010 Board of the Foundation of the Scandinavian Journal of Statistics. Published by Blackwell Publishing Ltd.
The Dantzig Selector in Cox's Proportional
Hazards Model
ANESTIS ANTONIADIS
D´epartement de Statistique, Universit´e Joseph Fourier
PIOTR FRYZLEWICZ
Department of Statistics, London School of Economics
FRÉDÉRIQUE LETUÉ
D´epartement de Statistique, Universit´e Pierre Mend`es France
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

  

Source: Antoniadis, Anestis - Laboratoire Jean Kuntzmann, Université Joseph Fourier

 

Collections: Mathematics