JSM 2011 Online Program

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Abstract Details

Activity Number: 179
Type: Contributed
Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
Sponsor: ENAR
Abstract - #301186
Title: A New Model-Free Sure Independence Screening for Ultra-High Dimensional Problems
Author(s): Runze Li and Wei Zhong*+ and Liping Zhu
Companies: Penn State University and Penn State University and Shanghai University of Finance and Economics
Address: 333 Thomas Building, University Park, PA, 16802,
Keywords: Variable Selection ; Sure Screening Property ; Ranking Consistency ; Distance Correlation ; Ultrahigh Dimensionality ; Dimension Reduction
Abstract:

High dimensional regression analysis has become increasingly important in diverse fields of scientific research. In this paper we introduce a new model-free sure independent screening procedure to select important predictors when p >> n. It also allows us consider independent screening for group-wise predictors and multivariate responses. This proposed procedure imposes little assumption on regression structure, so it also allows arbitrary regression relationship between y and x. For theoretical properties, we demonstrate that the proposed independent screening procedure enjoys the ranking consistency property, that is, it can rank important predictors in the top consistently even when p>>n. Meanwhile, under some mild conditions, it has the sure screening property, that is, with a proper threshold, it can select all important predictors with probability approaching to one as n goes to infinity. In addition, a corresponding iterative procedure is proposed to enhance its finite sample performance. Numerical examples through comprehensive simulations and an application indicate that the new proposal performs quite well in a variety of ultrahigh dimensional regressions.


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