B1212
Title: Robust regression in high dimensions: Sparse S- and MM-estimation
Authors: Andreas Alfons - Erasmus University Rotterdam (Netherlands) [presenting]
Viktoria Oellerer - KU Leuven (Belgium)
Christophe Croux - Leuven (Belgium)
Abstract: The S-estimator and the MM-estimator are frequently used regression estimators that are robust against the presence of outliers. While both estimators are highly robust, the latter also attains high efficiency. A drawback of those methods is that they cannot be applied to high-dimensional data, i.e., data with more variables than observations. By adding an $L_1$ penalty on the coefficient estimates to the respective objective functions, the sparse S-estimator and the sparse MM-estimator are introduced. These new estimators combine robust regression with sparse model estimation. In addition to deriving the breakdown point and the influence function, the performance of sparse S and sparse MM is assessed by means of a simulation study.
