Another look at Huber's estimator: A new minimax estimator in regression with stochastically bounded noise

Xuelei Sherry Ni, Xiaoming Huo
2009 Journal of Statistical Planning and Inference  
Huber's estimator 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
more » ... 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-theart 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.
doi:10.1016/j.jspi.2008.03.040 fatcat:wj6ndh7r3na5de7m7top3riqw4