Robust Signal Recovery for High-Dimensional Linear Log-Contrast Models with Compositional Covariates
针对误差分布可能重尾且不对称的高维线性对数对比模型，提出基于Huber损失和L1惩罚的稳健信号恢复方法，证明了估计量的相合性和符号支持恢复的高概率性质，并通过GDP满意度和HIV微生物组数据验证。
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.