Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariates
arXiv:2206.07594v35 citationsh-index: 4
Originality Incremental advance
AI Analysis
This addresses robust regression for data with heavy tails and outliers, which is incremental as it builds on existing robust estimation methods.
The paper tackles robust and sparse estimation of linear regression coefficients when both covariates and noises are heavy-tailed and contaminated by outliers, achieving an error bound that is nearly optimal.
Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are contaminated by malicious outliers. Our estimator can be computed efficiently. Further, the error bound of the estimator is nearly optimal.