Title: Sparse robust regression estimators
Authors: David Kepplinger - University of British Columbia (Canada)
Matias Salibian-Barrera - The University of British Columbia (Canada)
Gabriela Cohen Freue - University of British Columbia (Canada) [presenting]
Abstract: In many current applications scientists can easily measure a very large number of variables (for example, several thousands of gene expression levels) some of which are expected be useful to explain or predict a specific response variable of interest. These potential explanatory variables are most likely to contain redundant or irrelevant information, and in many cases, their quality and reliability may be suspect. We developed a penalized robust regression estimator that can be used to identify a useful subset of explanatory variables to predict the response, while protecting the resulting estimator against possible aberrant observations in the data set. Using an Elastic Net penalty, the proposed estimator can be used to select variables, even in cases with more variables than observations or when many of the candidate explanatory variables are correlated. We present the new estimator and an algorithm to compute it. We also illustrate performance of the proposed estimator in a simulation study and a real data set.