Penalized Rank Regression Using Adjusted Adaptive Lasso

• Activity Number: 131
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Asuman Turkmen*+ and Omer Ozturk
• Companies: Ohio State University and Ohio State University
• Keywords: Multicollinearity ; Rank regression ; Adaptive Lasso ; Variable selection

Abstract

Many different types of penalties have been introduced to achieve variable selection in least squares (LS) analysis. It is well known that the LS method is sensitive to outliers and heavy tailed error distributions, and consequently, these may present serious problems for the least squares based methods in variable selection. Since rank based procedures have desirable robustness properties compared to LS procedures, we propose a rank based adaptive LASSO-type penalized regression estimator and variable selection procedure in linear regression models. The proposed estimator and variable selection procedure are robust against outliers in both the response and predictor space. Furthermore, since rank regression can yield unstable estimators in the presence of multicollinearity, to provide robust inference against multicollinearity, we adjust the penalty term in the adaptive lasso function by incorporating the standard errors of the rank estimator. The theoretical properties of the proposed procedures are established and their performances are investigated through a simulation study and a real data application using the Plasma Beta-Carotene Level data set.