Stein estimation for non-normal spherically symmetric location families in three dimensions
type: Item
instance of: scholarly article
title: Stein estimation for non-normal spherically symmetric location families in three dimensions
zbMATH Open document ID: 0779.62048
DOI: 10.1016/0047-259X(92)90077-S
author: Ann Cohen Brandwein
author: Stefan S. Ralescu
author: William E. Strawderman
published in: Journal of Multivariate Analysis
publication date: 1993-09-01T00:00:00Z
review text: Suppose the random vector \(X=(X_ 1,X_ 2,X_ 3)'\) has density \(f(\| X-\theta\|^ 2)\) for \(\| X-\theta\|^ 2>R\) with \(f(t)\leq M<\infty\). The authors use Stein's integration by parts technique to find estimators of \(\theta\), with respect to quadratic loss. They find values of \(a\) for which the James-Stein estimator \(\delta_ a(x)=(1-a/X'X)X\) and \(\delta_{a,r}(x)=(1-a(Y(X'X)/X'X))X\) improve on \(X\).
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 404623
zbMATH Keywords: squared error loss
zbMATH Keywords: Stein's integration by parts technique
zbMATH Keywords: quadratic loss
zbMATH Keywords: James-Stein estimator
reviewed by: Songgui Wang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 404623