Minimax estimation of the mean of a general distribution when the parameter space is restricted
type: Item
instance of: scholarly article
title: Minimax estimation of the mean of a general distribution when the parameter space is restricted
zbMATH Open document ID: 0621.62030
author: Avraham A. Melkman
author: Yaacov Ritov
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: Consider the one-dimensional additive model \(Y=\theta +X\) where \(| \theta | \leq s\) and X has a specified distribution with \(EX=0\), \(EX^ 2=1\) and \(EX^ 4<\infty\). The authors study minimax estimation of mean \(\theta\). They extend results obtained by \textit{P. J. Bickel}, Ann. Stat. 9, 1301-1309 (1981; Zbl 0484.62013) for minimax estimation of the mean of a normal distribution when the parameter space is restricted. They obtain a class of estimators which are asymptotically minimax for \(\theta\) and show that the results obtained by Bickel remain valid without the normality assumption.
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 4007462
zbMATH Keywords: restricted parameter space
zbMATH Keywords: mean estimation
zbMATH Keywords: one-dimensional additive model
zbMATH Keywords: minimax estimation
zbMATH Keywords: asymptotically minimax
reviewed by: B. L. S. Prakasa Rao
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350278
OpenAlex ID: W1989466605
DOI: 10.1214/AOS/1176350278
description: scientific article; zbMATH DE number 4007462