Conditional Sure Independence Screening

• Activity Number: 466
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Emre Barut*+ and Jianqing Fan and Anneleen Verhasselt
• Companies: Princeton University and Princeton University and University of Antwerp
• Keywords: High Dimensional Statistics ; Variable Selection ; Sure Screening ; Generalized Linear Model ; GLM

Abstract

Independence screening is a powerful method for variable selection when the number of variables is massive. Fan and Lv (2008) propose a sure independence screening technique based on the correlation ranking. In many applications, researchers often have some prior knowledge that certain set of the variables are related to the response. In such a situation, a natural assessment on the relative importance of the other predictors is the conditional contributions of the individual predictors in presence of the known set of variables. This results in the conditional sure independence screening (CSIS). The conditioning reduces the false positive and false negative rates in the variable selection process. In this paper, we propose and study CSIS in the context of generalized linear models. For ultrahigh-dimensional statistical problems, we give the conditions under which the sure screening is possible and derive an upper bound on the number of the selected variables. We also spell out the situation under which CSIS yields a model selection consistency. Moreover, we provide two data-driven methods to select the thresholding parameter of the conditional screening.