Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model

Stephen J. Haslett; Jarkko Isotalo; Simo Puntanen

doi:10.12697/ACUTM.2021.25.16

Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model

Stephen J. Haslett
, Jarkko Isotalo
, Simo Puntanen

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this article we consider the partitioned fixed linear model F: Y = X₁β₁+ X₂β₂ + ε" and the corresponding mixed model M: Y =X₁β₁+X₂u+ ε, where ε is a random error vector and u is a random effect vector. In 2006, Isotalo, M¨ols, and Puntanen found conditions under which an arbitrary representation of the best linear unbiased estimator (BLUE) of an estimable parametric function of β₁in the fixed model F remains BLUE in the mixed model M. In this paper we extend the results concerning further equalities arising from models F and M.

Original language	English
Pages (from-to)	239-257
Number of pages	19
Journal	Acta et Commentationes Universitatis Tartuensis de Mathematica
Volume	25
Issue number	2
DOIs	https://doi.org/10.12697/ACUTM.2021.25.16
Publication status	Published - 19 Nov 2021

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AU - Haslett, Stephen J.

AU - Isotalo, Jarkko

AU - Puntanen, Simo

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AB - In this article we consider the partitioned fixed linear model F: Y = X1β1+ X2β2 + ε" and the corresponding mixed model M: Y =X1β1+X2u+ ε, where ε is a random error vector and u is a random effect vector. In 2006, Isotalo, M¨ols, and Puntanen found conditions under which an arbitrary representation of the best linear unbiased estimator (BLUE) of an estimable parametric function of β1in the fixed model F remains BLUE in the mixed model M. In this paper we extend the results concerning further equalities arising from models F and M.

KW - BLUE

KW - BLUP

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KW - Best linear unbiased predictor

KW - Equality of the BLUEs

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JO - Acta et Commentationes Universitatis Tartuensis de Mathematica

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ER -

Equalities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model

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