Estimation in models with commutative orthogonal block structure

Francisco Carvalho, João T. Mexia, Manuela M. Oliveira

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


A model with variance-covariance matrix V =(Formula Presented)Pi, where P1; : : : ;Pv are known pairwise orthogonal orthogonal projection matrices, will have Orthogonal Block Structure with variance components s (Formula Presented. Moreover, if matrices P1,……,.Pv commute with the orthogonal projection matrix T on the space spanned by the mean vector, the model will have Commutative Orthogonal Block Structure (COBS). In this paper we will use Commutative Jordan Algebras to study the algebraic properties of these models as well as optimal estimators. We show that once normality is assumed, sufficient complete statistics are obtained and estimators are Uniformly Minimum Variance Unbiased Estimators. AMS Subject Classification: 62J12.

Original languageEnglish
Pages (from-to)523-533
Number of pages11
JournalJournal of Statistical Theory and Practice
Issue number2
Publication statusPublished - 2009


  • Commutative Jordan algebras
  • Commutative orthogonal block structure
  • Mixed linear models
  • Variance components


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