Optimal estimators in biadditive models and their families

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.