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ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Statistics and Probability
Volume 11 - 2025 | doi: 10.3389/fams.2025.1379210
Optimal estimators in Biadditive models and their families
Provisionally accepted- 1 Departamento de Matemática, Escola de Ciência e Tecnologia, Universidade de Évora, Évora, Portugal
- 2 Department of Mechatronics Engineering, University of Évora,, Évora, Portugal
- 3 Institute of Contemporary History, Faculty of Social and Human Sciences, New University of Lisbon, Lisboa, Portugal
- 4 Center for Mathematics and Applications, Faculty of Sciences and Technology, New University of Lisbon, Caparica, Portugal
Biadditive regression models are linear models with an additive structure for their covariance matrix. In their study the use of commutative orthogonal structures is highly convenient as we show. We introduce commutative conditions and derive optimal estimators, namely Best Linear Unbiased Estimators (BLUE) and Best Quadratic Unbiased Estimators (BQUE). As applications of our results, prime basis factorials satisfy those commutative conditions and then families of such models have interesting properties.
Keywords: Biadditive Regression Models, Cumulants, heteroscedasticity, Optimum Estimators, Orthogonal block structure, Commutative orthogonal block structure
Received: 30 Jan 2024; Accepted: 17 Mar 2025.
Copyright: © 2025 Oliveira, Garção, Alexandre, Paulino and Oliveira. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Manuela Oliveira, Departamento de Matemática, Escola de Ciência e Tecnologia, Universidade de Évora, Évora, Portugal
Manuela Oliveira, Center for Mathematics and Applications, Faculty of Sciences and Technology, New University of Lisbon, Caparica, Portugal
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