Open AccessSimultaneous optimal predictions under two seemingly unrelated linear random-effects models
Author(s) -
Yongge Tian,
Pengyang Xie
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2020168
Subject(s) - context (archaeology) , mixed model , random effects model , variety (cybernetics) , linear model , mathematics , quadratic equation , matrix (chemical analysis) , best linear unbiased prediction , computer science , mathematical optimization , statistics , econometrics , machine learning , medicine , paleontology , meta analysis , geometry , biology , selection (genetic algorithm) , materials science , composite material
This paper considers simultaneous optimal prediction and estimation problems in the context of linear random-effects models. Assume a pair of seemingly unrelated linear random-effects models (SULREMs) with the random-effects and the error terms correlated. Our aim is to find analytical formulas for calculating best linear unbiased predictors (BLUPs) of all unknown parameters in the two models by means of solving a constrained quadratic matrix optimization problem in the Löwner sense. We also present a variety of theoretical and statistical properties of the BLUPs under the two models.