The Dantzig Selector in Cox's Proportional Hazards Model

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.     

Testing the Equality of Covariance Operators in Functional Samples

Abstract. We propose a non‐parametric test for the equality of the covariance structures in two functional samples. The test statistic has a chi‐square asymptotic distribution with a known number of degrees of freedom, which depends on the level of dimension reduction needed to represent the data. Detailed analysis of the asymptotic properties is developed. Finite sample perfo‐rmance is examined by a simulation study and an application to egg‐laying curves of fruit flies.