Properties of BLUEs in full versus small linear models

Haslett, Stephen; Markiewicz, Augustyn; Puntanen, Simo

doi:10.1080/03610926.2022.2052899

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2023

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Cited by 2 publications

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“…In this article we focus on characterizing the mutual relations between the sets V 1 and V 1/12 . The relations between the sets V 1 and V 12 were studied by Haslett et al [2] and Haslett and Puntanen [4].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Further remarks on permissible covariance structures for simultaneous retention of BLUEs in linear models

Puntanen

Haslett

Isotalo

et al. 2023

ACUTM

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We consider the partitioned linear model M12(V0) = { y, X1β1 + X2 β2, V0 } and the corresponding small model M1(V0) = { y, X1β1 , V0 } . We define the set V1/12 of nonnegative definite matrices V such that every representation of the best linear unbiased estimator, BLUE, of μ1 = X1β1 under M12(V0) remains BLUE under M12(V) . Correspondingly, we can characterize the set V1 of matrices V such that every BLUE of μ1 = X1β1 under M1(V0) remains BLUE under M1(V). In this paper we focus on the mutual relations between the sets V1 and V1/12 .

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Section: Discussionmentioning

confidence: 99%

“…The relations between the sets V 1 and V 12 were studied by Haslett et al [2] and Haslett and Puntanen [4]. □ Remark 1.3.…”

Section: Introductionmentioning

confidence: 99%