Robust Sparse Regression with High-Breakdown Value

Abstract

Penalized least squares estimators are sensitive to the influence of outliers like the ordinary least squares estimator. We propose a sparse regression estimator for robust variable selection and estimation based on a robust initial estimator. It is proven that our estimator has at least the same breakdown value as the initial estimator. Numerical examples are presented to illustrate our method.

Keywords:

• Adaptive estimation
• Breakdown value
• Non negative garrote
• Variable selection

Mathematics Subject Classification:

• 62F35; 62J07