Improved confidence sets for the coefficients of a linear model with spherically symmetric errors
type: Item
instance of: scholarly article
title: Improved confidence sets for the coefficients of a linear model with spherically symmetric errors
zbMATH Open document ID: 0601.62048
author: Jiunn Tzon Hwang
author: Jeesen Chen
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: The authors consider a linear model \(Y=A\theta +\sigma \cdot \epsilon\) where the pdf of \(\epsilon\) is assumed to be spherically symmetric around zero and with finite variance-covariance matrix. They obtain confidence sets for the location parameter \(\theta\) using the James-Stein estimator for \(\theta\) when the \(\dim(\theta)\geq 3\) and show that the James-Stein confidence dominates the classical confidence sets with the same radius not only when error distribution is \(N(0,\sigma^ 2I)\) but also for uniform distribution, double exponential and multivariate t distribution.
reviewed by: B. K. Kale
Mathematics Subject Classification ID: 62F25
Mathematics Subject Classification ID: 62J07
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 62F35
zbMATH DE Number: 3969886
zbMATH Keywords: coverage probability
zbMATH Keywords: dominance
zbMATH Keywords: fixed radius
zbMATH Keywords: linear model
zbMATH Keywords: spherically symmetric
zbMATH Keywords: confidence sets
zbMATH Keywords: location parameter
zbMATH Keywords: James-Stein estimator
zbMATH Keywords: uniform distribution
zbMATH Keywords: double exponential
zbMATH Keywords: multivariate t distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349932
OpenAlex ID: W2024650258
DOI: 10.1214/AOS/1176349932
description: scientific article; zbMATH DE number 3969886