Consistency of the Elastic Net under a finite second moment assumption on the noise

Abstract

Elastic Net regularization is a powerful tool to do prediction as well as variable selection. De Mol et al. (2009) developed a theoretical framework to analyse the Elastic Net and proved important properties as the consistency of the Elastic Net estimator under certain model assumptions. In this paper, these assumptions are relaxed and extended to a wider class of noise distributions. It is shown that the consistency of the Elastic Net still holds true under a finite second moment assumption on the noise term.