An identity concerning a Wishart matrix
type: Item
instance of: scholarly article
title: An identity concerning a Wishart matrix
zbMATH Open document ID: 0588.62069
DOI: 10.1007/BF01894727
author: B. George
published in: Metrika
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176030
review text: Let S be a \(p\times p\) Wishart matrix with parameters n and \(\Sigma\). For a rational number \(\alpha =r/s\) with r and s integers and s positive, let \(S^{\alpha}\) denote a positive definite matrix such that \((S^{\alpha})^ s=S^ r\). Using a decision theoretic argument, we prove that \[ E[(tr S)^ 2tr S^{\alpha}]=(np+2+2\alpha)E[tr S tr S^{\alpha}] \] when \(\Sigma =I\) and \(np+2+2\alpha\) is positive.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62C10
zbMATH DE Number: 3945095
zbMATH Keywords: Bayes estimator
zbMATH Keywords: Wishart matrix
MaRDI profile type: Publication
cites work: Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach
cites work: Q5532825
description: scientific article; zbMATH DE number 3945095