Title: Sparse S- and MM-estimation for high-dimensional regression
Authors: Andreas Alfons - Erasmus University Rotterdam (Netherlands) [presenting]
Christophe Croux - Edhec Business School (France)
Viktoria Oellerer - KU Leuven (Belgium)
Abstract: The S-estimator and the MM-estimator are among the most popular robust regression estimators. While both estimators are highly robust against outliers in the data, the latter has the advantage of also attaining high efficiency. However, those methods cannot be applied to high-dimensional data, i.e. data with more variables than observations. As a remedy, the sparse S-estimator and the sparse MM-estimator are defined by adding an L1 penalty on the coefficient estimates to the respective objective functions. These new estimators combine robust regression with sparse model estimation, but fast algorithms are required for use in practical applications. In addition to presenting algorithms for the computation sparse S and sparse MM, their performance is assessed by means of a simulation study.