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Inference for types and structured families of commutative orthogonal block structures

Author

Listed:
  • Francisco Carvalho
  • João Mexia
  • Carla Santos
  • Célia Nunes

Abstract

Models with commutative orthogonal block structure, COBS, have orthogonal block structure, OBS, and their least square estimators for estimable vectors are, as it will be shown, best linear unbiased estimator, BLUE. Commutative Jordan algebras will be used to study the algebraic structure of the models and to define special types of models for which explicit expressions for the estimation of variance components are obtained. Once normality is assumed, inference using pivot variables is quite straightforward. To illustrate this class of models we will present unbalanced examples before considering families of models. When the models in a family correspond to the treatments of a base design, the family is structured. It will be shown how, under quite general conditions, the action of the factors in the base design on estimable vectors, can be studied. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Francisco Carvalho & João Mexia & Carla Santos & Célia Nunes, 2015. "Inference for types and structured families of commutative orthogonal block structures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 337-372, April.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:3:p:337-372
    DOI: 10.1007/s00184-014-0506-8
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    References listed on IDEAS

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    1. Mexia, Joao Tiago, 1990. "Best linear unbiased estimates, duality of F tests and the Scheffe multiple comparison method in the presence of controlled heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 271-281, December.
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