2009/06/18 by Wenhua Jiang, Cun-Hui Zhang, Cun‐Hui Zhang · 2 citations
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Applied mathematics #Bayes estimator #Bayes' theorem #Bayesian probability #Combinatorics #Estimator #Mathematical optimization #Mathematics #Maximum likelihood #Mean squared error #Minimax #Minimax estimator #Moment (physics) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #math.ST #msc:62C12 #msc:62C25 #msc:62G05 #msc:62G08 #msc:62G20 #stat.TH
paper · pdf · doi:10.1214/08-aos638
published as Annals of Statistics 2009, Vol. 37, No. 4, 1647-1684 · Published in at http://dx.doi.org/10.1214/08-AOS638 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2009/06/18 · arxiv created 2009/08/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions on the unknown means, the average mean squared error (MSE) of the GMLEB is within an infinitesimal fraction of the minimum average MSE among all separable estimators which use a single deterministic estimating function on individual observations, provided that the risk is of greater order than (log n)5/n. We also prove that the GMLEB is uniformly approximately minimax in regular and weak ℓp balls when the order of the length-normalized norm of the unknown means is between (log n)κ1/n1/(p∧2) and n/(log n)κ2. Simulation experiments demonstrate that the GMLEB outperforms the James–Stein and several state-of-the-art threshold estimators in a wide range of settings without much down side.