Minimax estimates of a normal mean vector for arbitrary quadratic loss and unknown covariance matrix
type: Item
instance of: scholarly article
title: Minimax estimates of a normal mean vector for arbitrary quadratic loss and unknown covariance matrix
zbMATH Open document ID: 0613.62004
author: Leon Jay Gleser
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: The purpose of this paper is to find a class of estimators which dominate the usual estimator X of the mean vector \(\mu\) of a multivariate normal distribution under arbitrary quadratic loss in the case where the covariance matrix is unknown. The integration-by-parts methods for both the multivariate normal and Wishart distributions are combined to yield unbiased estimates of risk difference (versus X) for certain classes of estimators, defined indirectly through a ''seed'' function dependent upon X and an independent Wishart matrix. In this way we obtain a new class of minimax estimators of \(\mu\) which is closely related to classes of estimators considered in \textit{J. Berger} and \textit{L. R. Haff}, Stat. Decis. 1, 105-129 (1983; Zbl 0562.62005) and by the author, Ann. Stat. 7, 838-846 (1979; Zbl 0418.62004).
reviewed by: Krzysztof Piasecki
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62H99
zbMATH DE Number: 3992613
zbMATH Keywords: unknown covariance matrix
zbMATH Keywords: seed function
zbMATH Keywords: mean vector
zbMATH Keywords: multivariate normal
zbMATH Keywords: quadratic loss
zbMATH Keywords: integration-by-parts methods
zbMATH Keywords: Wishart distributions
zbMATH Keywords: risk difference
zbMATH Keywords: minimax estimators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350184
OpenAlex ID: W4237225570
DOI: 10.1214/AOS/1176350184
description: scientific article; zbMATH DE number 3992613