Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters

Improving on Minimum Risk Equivariant and Linear Minimax Estimators of Bounded Multivariate Location Parameters

We propose improvements under squared error loss of the minimum risk equivariant and the linear minimax estimators for estimating the location parameter θ of a p-variate spherically symmetric distribution, with θ restricted to a ball of radius m centered at the origin. Our construction of explicit...

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Bibliographic Details
Main Authors: Éric Marchand, Amir T. Payandeh Najafabadi
Format: Article
Language:English
Published: Instituto Nacional de Estatística | Statistics Portugal 2010-11-01
Series:Revstat Statistical Journal
Subjects:
decision theory
spherical symmetric distribution
restricted parameter
minimum risk equivariant estimator
linear minimax estimator
dominating estimators
Online Access:https://revstat.ine.pt/index.php/REVSTAT/article/view/93
Description
Summary:We propose improvements under squared error loss of the minimum risk equivariant and the linear minimax estimators for estimating the location parameter θ of a p-variate spherically symmetric distribution, with θ restricted to a ball of radius m centered at the origin. Our construction of explicit improvements relies on a multivariate version of Kubokawa’s Integral Expression of Risk Difference (IERD) method. Applications are given for univariate distributions, for the multivariate normal, and for scale mixture of multivariate normal distributions.
ISSN:1645-6726
2183-0371

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