Jordan algebras and Bayesian quadratic estimation of variance components
type: Item
instance of: scholarly article
title: Jordan algebras and Bayesian quadratic estimation of variance components
zbMATH Open document ID: 0760.62068
DOI: 10.1016/0024-3795(92)90297-N
author: Hilmar Drygas
author: Roman Zmyślony
published in: Linear Algebra and its Applications
publication date: 1992-09-27T00:00:00Z
review text: In a variance-component model there are in general no uniformly best (quadratic) unbiased estimators for linear functions of variance components. \textit{J. Seely} [Ann. Math. Statistics 42, 710-721 (1971; Zbl 0249.62067)] has found a necessary and sufficient condition for their existence. He found that a certain class of square matrices should form a Jordan algebra, or, as he called it, a quadratic subspace. This condition is in particular met if the variance-component model under investigation is a balanced mixed linear model. It is the purpose of this paper to give some properties of Jordan algebras: simple formulae for \(A\circ B\), \(A^ +\), \(A^ -\); solutions of matrix equations \(AXB=C\), and so on. Applications are the determination of locally optimal estimators and Bayesian quadratic estimators of variance components.
Mathematics Subject Classification ID: 62J10
Mathematics Subject Classification ID: 17C99
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 57572
zbMATH Keywords: uniformly best quadratic unbiased estimators
zbMATH Keywords: linear functions of variance components
zbMATH Keywords: Jordan algebra
zbMATH Keywords: quadratic subspace
zbMATH Keywords: balanced mixed linear model
zbMATH Keywords: locally optimal estimators
zbMATH Keywords: Bayesian quadratic estimators of variance components
MaRDI profile type: Publication
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full work available at URL: 0024-3795(92)90297-n
OpenAlex ID: W2116411414
description: scientific article; zbMATH DE number 57572