Robust and sparse estimation methods for high dimensional linear and logistic regression

摘要

Fully robust versions of the elastic net estimator are introduced for linearand logistic regression. The algorithms to compute the estimators are based onthe idea of repeatedly applying the non-robust classical estimators to datasubsets only. It is shown how outlier-free subsets can be identifiedefficiently, and how appropriate tuning parameters for the elastic netpenalties can be selected. A final reweighting step improves the efficiency ofthe estimators. Simulation studies compare with non-robust and other competingrobust estimators and reveal the superiority of the newly proposed methods.This is also supported by a reasonable computation time and by good performancein real data examples.