We consider outlier-robust and sparse estimation of linear regression coefficients, when covariate vectors and noises are sampled, respectively, from an $\mathfrak{L}$-subGaussian distribution and a heavy-tailed distribution. Additionally, the covariate vectors and noises are contaminated by adversarial outliers. We deal with two cases: the covariance matrix of the covariates is known or unknown. Particularly, in the known case, our estimator can attain a nearly information theoretical optimal error bound, and our error bound is sharper than those of earlier studies dealing with similar situations. Our estimator analysis relies heavily on generic chaining to derive sharp error bounds.

翻译：我们认为,当从一个美元=mathfrak{L}$u-subGausian的分布和重尾分布中分别对共变矢量和噪声进行抽样取样时,共变矢量和噪声会受到对抗性离子的污染。我们处理两种情况:共变量的共变量矩阵是已知的或未知的。特别是,在已知的情况下,我们的估量器可以达到几乎信息理论上的最佳误差,我们的误差约束比处理类似情况的早期研究的误差范围要明确得多。我们的估测器分析严重依赖一般链条来得出尖锐的误差界限。