Robust Variable Selection with Exponential Squared Loss
Speaker:Prof. Xueqin Wang
School of Mathematics and Computational Science
Sun Yat-sen University
Date & Time:25 Oct 2012 (Thursday) 10:30
Organized by:Department of Mathematics


Robust variable selection procedures through penalized regression has been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness, while maintaining its numerical performance. Specifically, under defined regularity conditions, our estimators are -consistent and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed methods with a recent method, using the oracle estimator as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error, the positive selection rate, and the non-causal selection rate even in the presence of influential points. In contrast, the other existing procedure has a much lower non-causal selection rate. Furthermore, we re-analyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Data that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods.


Prof. Xueqin Wang is currently the Professor of School of Mathematics and Computational Science, the Deputy Chair of Department of Statistical Science and the Guest Professor of Zhongshan Ophthalmic Center and State Key Laboratory of Ophthalmology, at Sun Yat-sen University. Prof. Wang obtained his Ph.D. at State University of New York, Binghamton. He is awarded First prize in the 8th Outstanding Achievement Award in Statistical Research by Statistical Society of Guangdong in 2010. The recent publication of Prof. Wang include, Genetic Association Test for Multiple Traits at Gene Level, Evaluation of Anterior Segment Changes During Accommodation in Young and Presbyopic Populations Using Pentacam HR System, Statistical inference of biometrical genetic model with cultural transmission and Low serum apolipoprotein A1B ratio is associated with proliferative diabetic retinopathy in type 2 diabetes etc.