Selecting a minimax estimator doing well at a point
type: Item
instance of: scholarly article
title: Selecting a minimax estimator doing well at a point
zbMATH Open document ID: 0604.62044
DOI: 10.1016/0047-259X(86)90091-6
published in: Journal of Multivariate Analysis
publication date: 1986-01-01T00:00:00Z
review text: Let \(X_ i\sim N(\theta_ i,I_ p)\), \(i=1,...,n\) \((n>p+1\), \(p>1)\) be an independent finite sequence of p-dimensional vectors. Let \(X=(X_ 1,...,X_ n)\) be a \(p\times n\) matrix of random variables with matrix of means \(\theta =(\theta_ 1,...,\theta_ n)\). Stein estimator is of the form \(\delta (X)=X+\nabla \ln f(\ell)\), where \(\ell =(\ell_ 1,...,\ell_ p)'\) is a vector with components \(\ell_ 1\geq \ell_ 2\geq...\geq \ell_ p>0\), the characteristic roots of \(S=XX'\), and \(\nabla \ln f(\ell)=((\partial /\partial X_{jk})\ln f(\ell))\) is the matrix of partial derivatives of the function ln f(\(\ell)\). In this paper the author gives an estimator \(\delta^*(X)\) which dominates \(\delta\) (X) such that the estimator is the best at \(\theta =0\) among estimators \(\delta_{\beta}(X)=\delta (X)-2X/(tr S/(p(p+1)-2)+\beta (\ell)\), where \(\beta\) is in a certain class.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 3976110
zbMATH Keywords: minimax estimator
zbMATH Keywords: dominating estimator
zbMATH Keywords: Stein estimator
author: Zukang Zheng
reviewed by: Arjun K. Gupta
MaRDI profile type: Publication
cites work: Q3255781
cites work: Empirical Bayes on vector observations: An extension of Stein's method
cites work: Q4130201
cites work: On estimation of matrix of normal mean
description: scientific article; zbMATH DE number 3976110