Nonnegative unbiased estimability of linear combinations of two variance components
type: Item
instance of: scholarly article
title: Nonnegative unbiased estimability of linear combinations of two variance components
zbMATH Open document ID: 0563.62045
DOI: 10.1016/0378-3758(84)90027-2
author: Anna Molińska
author: Jerzy K. Baksalary
published in: Journal of Statistical Planning and Inference
publication date: 1984-01-01T00:00:00Z
review text: For a general mixed model with two variance components \(\theta_ 1\) and \(\theta_ 2\), a criterion for a function \(q_ 1\theta_ 1+q_ 2\theta_ 2\) to admit an unbiased nonnegative definite quadratic estimator is established in a form that allows answering the question of existence of such an estimator more explicitly than with the use of the criteria known hitherto. An application of this result to the case of a random one-way model shows that for many unbalanced models the estimability criterion is expressible directly by the largest of the numbers of observations within levels, thus extending the criterion established by \textit{L. R. LaMotte} [J. Am. Stat. Assoc. 68, 728-730 (1973; Zbl 0271.62093)] for balanced models.
Mathematics Subject Classification ID: 62J10
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 3898041
zbMATH Keywords: general mixed model
zbMATH Keywords: unbiased nonnegative definite quadratic estimator
zbMATH Keywords: random one-way model
zbMATH Keywords: unbalanced models
zbMATH Keywords: estimability
MaRDI profile type: Publication
full work available at URL: 0378-3758(84)90027-2
OpenAlex ID: W2064449409
cites work: On Non-Negative Quadratic Unbiased Estimation of Variance Components
cites work: Invariant Quadratic Estimators in the Random, One-Way ANOVA Model
cites work: On the existence of unbiased nonnegative estimates of variance covariance components
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description: scientific article; zbMATH DE number 3898041