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

Dongxiao Han, Jian Huang, Yuanyuan Lin, Lei Liu, Lianqiang Qu and Liuquan Sun

Journal of Business & Economic Statistics, 2023, vol. 41, issue 3, 957-967

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 ℓ1 penalization. We establish the ℓ1 and ℓ2 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:41:y:2023:i:3:p:957-967

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DOI: 10.1080/07350015.2022.2097911

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