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

Authors

DOI:

https://doi.org/10.12697/ACUTM.2023.27.09

Keywords:

Best linear unbiased estimator, BLUE, covariance matrix, equality of the BLUEs, partitioned linear model

Abstract

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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Author Biographies

Stephen Haslett, Massey University, New Zealand

https://orcid.org/0000-0002-2775-5468

Jarkko Isotalo, Tampere University

https://orcid.org/0000-0002-8068-6262

Augustyn Markiewicz, Poznań University of Life Sciences

https://orcid.org/0000-0001-5473-3419

Simo Puntanen, Tampere University

https://orcid.org/0000-0002-6776-0173 

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Published

2023-05-28

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Section

Articles