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Elimination of nuisance parameters in a regression model. (English) Zbl 0605.62081
In a regression model (\(\xi\),(A,S)(\(\theta\) ’,\(\vartheta\) ’)’,\(\Sigma)\) with nuisance parameter \(\vartheta\) the class \({\mathcal T}=\{T:TA=A\), \(TS=0\}\) of eliminating transformations is investigated. An eliminating transformation T is optimal if the transformed model (T\(\xi\),A\(\theta\),T\(\Sigma\) T’) enables us to construct such a linear unbiased estimator of the vector \(A\theta\) which has the same covariance matrix as the covariance matrix of the best linear unbiased estimator in the original model. The class of optimal eliminating transformations is found.

62J99 Linear inference, regression
62J05 Linear regression; mixed models
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