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

  • Stephen Haslett Massey University; University of Wollongong; Australian National University
  • Jarkko Isotalo Tampere University
  • Simo Puntanen Tampere University
Keywords: best linear unbiased estimator, best linear unbiased predictor, BLUE, BLUP, equality of BLUEs, partitioned linear model

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 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.

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Author Biographies

Jarkko Isotalo, Tampere University

Faculty of Information Technology and Communication Sciences

Simo Puntanen, Tampere University

Faculty of Information Technology and Communication Sciences

Published
2021-11-17
Section
Articles