Robust Signal Recovery for High-Dimensional Linear Log-Contrast Models with Compositional Covariates

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 l(1) penalization. We establish the l(1) and l(2) 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.