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Robust and sparse estimation of linear regression coefficients isinvestigated. The situation addressed by the present paper is that covariatesand noises are sampled from heavy-tailed distributions, and the covariates andnoises are contaminated by malicious outliers. Our estimator can be computedefficiently. Further, the error bound of the estimator is nearly optimal.

Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariates