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1149.62013 Ni, Xuelei Sherry Huo, Xiaoming Another look at Huber's estimator: a new minimax estimator in regression with stochastically bounded noise. J. Stat. Plann. Inference 139, No. 2, 503-515 (2009). 2009 Elsevier Science B.V. (North-Holland), Amsterdam EN 62F12 62C20 62J05 65C60 90C90 62F35 Huber's estimator regression asymptotic minimax estimator Zbl 0536.62025

doi:10.1016/j.jspi.2008.03.040

Summary: {\it P. J. Huber}'s estimator [Robust statistics. New York etc.: Wiley (1981; Zbl 0536.62025)] has had a long lasting impact, particularly on robust statistics. It is well known that under certain conditions, Huber's estimator is asymptotically minimax. A moderate generalization in rederiving Huber's estimator shows that Huber's estimator is not the only choice. We develop an alternative asymptotic minimax estimator and name it regression with stochastically bounded noise (RSBN). Simulations demonstrate that RSBN is slightly better in performance, although it is unclear how to justify such an improvement theoretically. We propose two numerical solutions: an iterative numerical solution, which is extremely easy to implement and is based on the proximal point method; and a solution by applying state-of-the-art nonlinear optimization software packages, e.g., SNOPT. Contribution: the generalization of the variational approach is interesting and should be useful in deriving other asymptotic minimax estimators in other problems.