Improved Robust Estimation of the Residual Scale in High-Dimensional Problems with the Adaptive Elastic Net S-Estimator for Efficient Robust Penalized Linear Regression Methods

• Activity Number: 581 - Recent Advances in High-Dimensional Data Estimation and Prediction
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 AM
• Sponsor: Section on Statistical Computing
• Author(s): David Kepplinger* and Ezequiel Smucler and Gabriela V. Cohen Freue
• Companies: University of British Columbia and University of British Columbia and University of British Columbia
• Keywords: robust estimation; regularized estimation; penalized estimation; elastic net penalty

Abstract

Improving biomedical technology leads to the collection of increasingly large amounts of -omics data. To harness this information, for instance to identify biomarkers for a given disease, efficient statistical methods are necessary. Although penalized regression methods are among the most common tools for these applications, most of the methods use the square error loss which is susceptible to outlying observations. Recently proposed penalized robust regression methods, on the other hand, either have low efficiency or require a robust and accurate estimate of the error scale to achieve the promised robustness and high efficiency. We propose a penalized regression estimator combining the robust S-loss with an adaptive elastic net penalty. We show that this estimator is variable selection consistent under weak conditions. This in turn improves the estimate of the error scale compared to non-adaptive elastic net. We demonstrate in numerical experiments that the improved error scale estimate in combination with the M-loss and the adaptive elastic net penalty yields robust and simultaneously efficient penalized estimators of regression.