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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.

##### MSC:
 62J99 Linear inference, regression 62J05 Linear regression; mixed models
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##### References:
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