Abstract
In this article, we propose a robust signal recovery method for high-dimensional linear log-contrast models, when the error distribution could be heavy-tailed and asymmetric. The proposed method is built on the Huber loss with penalization. We establish the and consistency for the resulting estimator. Under conditions analogous to the irrepresentability condition and the minimum signal strength condition, we prove that the signed support of the slope parameter vector can be recovered with high probability. The finite-sample behavior of the proposed method is evaluated through simulation studies, and applications to a GDP satisfaction dataset an HIV microbiome dataset are provided.
Supplementary Materials
All proofs are provided in the supplementary materials.
Acknowledgments
The authors are grateful to the Editor, the Associate Editor and the anonymous reviewers for their professional review and constructive comments that lead to significant improvements in the article.