All-in-one Robust Estimator for the Gaussian Mean
Published in Annals of Statistics (to appear), 2021
This paper presents a new robust estimator called Iteratively Re-weighted Mean (IRM) which enjoys 5 key properties desired for a robust estimator: computationally tractable, equivariant under similarity transformations, have a breakdown point around $0.28$, minimax optimal (up to logarithmic factor) and asymptotically efficient. IRM is obtained by an iterative reweighting approach assigning weights by solving a convex optimization problem (SDP). Dimension-free non-asymptotic risk bound for the expected error of the proposed estimator is proved. The results are extended for sub-Gaussian distributions, as well as for unknown contamination level or unknown covariance matrix. Joint work with A. S. Dalalyan.