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Activity Number: 356
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #306925
Title: Robust Feature Screening and Selectionfor Ultrahigh Dimensional Heteroscedastic Single-Index Models
Author(s): Wei Zhong*+ and Runze Li and Liping Zhu
Companies: Penn State University and Penn State University and Shanghai University of Finance and Economics
Address: Department of Statistics, University Park, PA, 16802,

In this paper, we propose a two-stage feature screening and variable selection procedure to study the estimation of the index parameter in heteroscedastic single-index models with ultrahigh dimensional covariates. In the screening stage, we propose a robust independent ranking and screening (RIRS) procedure to reduce the ultrahigh dimensionality of the covariates to a moderate scale. Aside from its computational simplicity, the RIRS procedure maintains the ranking consistency property and the sure screening property. Therefore, in an asymptotic sense the RIRS procedure guarantees to retain all the truly active predictors. However, some inactive predictors may be selected as well. In the cleaning stage, we propose penalized linear quantile regression to refine the selection of the preceding RIRS procedure, and to simultaneously estimate the direction of the index parameter. We establish the consistency and the oracle property of the resulting penalized estimator, and demonstrate through comprehensive numerical studies that the two-stage estimation procedure is computationally expedient and presents an outstanding finite sample performance.

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