Open AccessEqualities between the BLUEs and BLUPs under the partitioned linear fixed model and the corresponding mixed model
Author(s) -
Stephen Haslett,
Jarkko Isotalo,
Simo Puntanen
Publication year - 2021
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2021.25.16
Subject(s) - mixed model , mathematics , random effects model , fixed effects model , estimator , linear model , generalized linear mixed model , best linear unbiased prediction , function (biology) , statistics , combinatorics , computer science , panel data , artificial intelligence , selection (genetic algorithm) , medicine , meta analysis , evolutionary biology , biology
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 β1 in 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.