Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models

Aníbal Areia, Francisco Carvalho, João T. Mexia

Research output: Contribution to journalReview article

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Abstract

We will discuss orthogonal models and error orthogonal models and their algebraic structure, using as background, commutative Jordan algebras. The role of perfect families of symmetric matrices will be emphasized, since they will play an important part in the construction of the estimators for the relevant parameters. Perfect families of symmetric matrices form a basis for the commutative Jordan algebra they generate. When normality is assumed, these perfect families of symmetric matrices will ensure that the models have complete and sufficient statistics. This will lead to uniformly minimum variance unbiased estimators for the relevant parameters.

Original languageEnglish
Pages (from-to)135-140
Number of pages6
JournalOpen Mathematics
Volume13
Issue number1
DOIs
Publication statusPublished - 1 Jan 2015

Fingerprint

Sufficient Statistics
Symmetric matrix
Jordan Algebra
Commutative Algebra
Uniformly Minimum Variance Unbiased Estimator
Algebraic Structure
Normality
Model
Estimator
Family

Keywords

  • Commutative Jordan algebras
  • Orthogonal models
  • Perfect families

Cite this

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abstract = "We will discuss orthogonal models and error orthogonal models and their algebraic structure, using as background, commutative Jordan algebras. The role of perfect families of symmetric matrices will be emphasized, since they will play an important part in the construction of the estimators for the relevant parameters. Perfect families of symmetric matrices form a basis for the commutative Jordan algebra they generate. When normality is assumed, these perfect families of symmetric matrices will ensure that the models have complete and sufficient statistics. This will lead to uniformly minimum variance unbiased estimators for the relevant parameters.",
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Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models. / Areia, Aníbal; Carvalho, Francisco; Mexia, João T.

In: Open Mathematics, Vol. 13, No. 1, 01.01.2015, p. 135-140.

Research output: Contribution to journalReview article

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AU - Carvalho, Francisco

AU - Mexia, João T.

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