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- W2092617044 abstract "Consider a general linear model for a column vector $y$ of data having $E(y) = X alpha$ and $operatorname{Var}(y) = sigma^2H$, where $alpha$ 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 $TH = phi$. The estimation of a linear function of $alpha$ 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 $alpha$ 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." @default.
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- W2092617044 date "1981-05-01" @default.
- W2092617044 modified "2023-09-25" @default.
- W2092617044 title "Unbiased and Minimum-Variance Unbiased Estimation of Estimable Functions for Fixed Linear Models with Arbitrary Covariance Structure" @default.
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- W2092617044 doi "https://doi.org/10.1214/aos/1176345467" @default.
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