Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliers
This addresses robust estimation in high-dimensional statistics for scenarios with non-standard data distributions, though it appears incremental as it builds on existing sparse regression methods.
The paper tackles the problem of estimating coefficients in sparse linear regression when both covariates and noises are heavy-tailed and contaminated by outliers, achieving sharp error bounds with efficient computation.
We investigate a problem estimating coefficients of linear regression under sparsity assumption when covariates and noises are sampled from heavy tailed distributions. Additionally, we consider the situation where not only covariates and noises are sampled from heavy tailed distributions but also contaminated by outliers. Our estimators can be computed efficiently, and exhibit sharp error bounds.