Robust Feature Screening and Selection for Ultrahigh-Dimensional Heteroscedastic Single-Index Models

• Activity Number: 5
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Runze Li*+ and Wei Zhong and Liping Zhu and Hengjian Cui
• Companies: Penn State and Xiamen University and Shanghai University of Finance and Economics and Capital Normal University
• Keywords: Heteroscedasticity ; penalized quantile regression ; single-index models ; sure screening property ; variable selection ; ultrahigh dimensionality

Abstract

A robust estimation approach for ultrahigh dimensional heteroscedastic single-index models will be introduced. We propose a penalized quantile regression method to study the estimation of the index parameter in heteroscedastic single-index models with high dimensional covariates. The resulting estimator is robust to the heteroscedasticity of the response and its consistency and oracle property have been established under milder conditions. When the dimension of covariates increases exponentially as the sample size, an independence screening procedure can be utilized before the regularization method to reduce the dimension to a moderate scale. We further propose a robust sure independence screening using distance correlation. The new screening procedure possesses several appealing advantages: (a) it is model-free in the same sense as the DC-SIS and thus robust to the model misspecification. (b) It is robust to heavy tails and extreme values in the response. (c) Its sure screening property is valid without any moment assumption of the response. The robust estimation approach is demonstrated to have good finite sample performance through simulation studies and a real data example.