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Operations with Iso-structured Models with Commutative Orthogonal Block Structure: An Introductory Approach

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Statistical Modelling and Risk Analysis (ICRA 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 430))

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Abstract

An approach to models based on an algebraic context allows interesting and useful statistical results to be derived or at least better understood. In the approach to models with commutative orthogonal block structure via algebraic structure it is possible to show that the orthogonal projection matrix in the space spanned by the mean vector commuting with the covariance matrix guarantees least squares estimators giving best linear unbiased estimators for estimable vectors. In this work we focus on the possibility of performing operations with models with commutative orthogonal block structure that are iso-structured, that is, models generating the same commutative Jordan Algebra of symmetric matrices.

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Acknowledgements

This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UIDB/00297/2020 and UIDB/00212/2020.

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Authors and Affiliations

  1. Polytechnic Institute of Beja, Campus IPBeja, Beja, Portugal

    Carla Santos

  2. NOVAMath-Center for Mathematics and Applications, SST, New University of Lisbon, Caparica Campus, Caparica, Portugal

    Carla Santos

  3. Polytechnic Institute of Portalegre, Campus Politécnico, Portalegre, Portugal

    Cristina Dias

  4. NOVAMath-Center for Mathematics and Applications, SST, New University of Lisbon, Caparica Campus, Caparica, Portugal

    Cristina Dias

  5. Department of Mathematics and Center of Mathematics and Applications, University of Beira Interior, Covilhã, Portugal

    Célia Nunes

  6. NOVAMath-Center for Mathematics and Applications, SST, New University of Lisbon, Caparica Campus, Caparica, Portugal

    João T. Mexia

Authors
  1. Carla Santos
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  2. Cristina Dias
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  3. Célia Nunes
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  4. João T. Mexia
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Corresponding author

Correspondence to Carla Santos .

Editor information

Editors and Affiliations

  1. Univeristy of West Attica, Egaleo, Greece

    Christos P. Kitsos

  2. Universidade Aberta, Lisboa, Portugal

    Teresa A. Oliveira

  3. University of Perugia, Perugia, Italy

    Francesca Pierri

  4. University of Salerno, Fisciano, Italy

    Marialuisa Restaino

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Santos, C., Dias, C., Nunes, C., Mexia, J.T. (2023). Operations with Iso-structured Models with Commutative Orthogonal Block Structure: An Introductory Approach. In: Kitsos, C.P., Oliveira, T.A., Pierri, F., Restaino, M. (eds) Statistical Modelling and Risk Analysis. ICRA 2022. Springer Proceedings in Mathematics & Statistics, vol 430. Springer, Cham. https://doi.org/10.1007/978-3-031-39864-3_13

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