AUTHOR=Oliveira Manuela , Garção Eugénio , Alexandre Armando , Paulino Joana , Mexia João 

TITLE=Optimal estimators in biadditive models and their families

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 11 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2025.1379210

DOI=10.3389/fams.2025.1379210

ISSN=2297-4687

ABSTRACT=Biadditive regression models are linear models with an additive structure for their covariance matrix. We introduce commutative conditions and derive optimal estimators, namely Best Linear Unbiased Estimators (BLUE) and Best Quadratic Unbiased Estimators (BQUE). We develop a simulation study to compare the variance components estimates obtained through the proposed approach with those derived from Analysis of Variance and Markov Chain Monte Carlo methods. This research highlights that commutative orthogonal structures in these models are highly convenient to strengthen inference.