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Media type:
E-Article
Title:
Unbiased and Minimum-Variance Unbiased Estimation of Estimable Functions for Fixed Linear Models with Arbitrary Covariance Structure
Contributor:
Harville, David A.
Published:
Institute of Mathematical Statistics, 1981
Published in:
The Annals of Statistics, 9 (1981) 3, Seite 633-637
Language:
English
ISSN:
0090-5364
Origination:
Footnote:
Description:
<p>Consider a general linear model for a column vector y of data having E(y) = X α and<tex-math>$\operatorname{Var}(y) = \sigma^2H$</tex-math>, where α is a vector of unknown parameters and X and H are given matrices that are possibly deficient in rank. Let b = Ty, where T is any matrix of maximum rank such that TH = φ. The estimation of a linear function of α by functions of the form c + a'y, where c and a are permitted to depend on b, is investigated. Allowing c and a to depend on b expands the class of unbiased estimators in a nontrivial way; however, it does not add to the class of linear functions of α that are estimable. Any minimum-variance unbiased estimator is identically [for y in the column space of (X, H)] equal to the estimator that has minimum variance among strictly linear unbiased estimators.</p>