# 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

### 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 language English 135-140 6 Open Mathematics 13 1 https://doi.org/10.1515/math-2015-0009 Published - 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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title = "Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models",
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

TY - JOUR

T1 - Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models

AU - Areia, Aníbal

AU - Carvalho, Francisco

AU - Mexia, João T.

N1 - Sem PDF. Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through Centro de Matematica e Aplicacoes (PEst-OE/MAT/UI0297/2014)

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

KW - Commutative Jordan algebras

KW - Orthogonal models

KW - Perfect families

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U2 - 10.1515/math-2015-0009

DO - 10.1515/math-2015-0009

M3 - Review article

VL - 13

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EP - 140

JO - Open Mathematics

JF - Open Mathematics

SN - 2391-5455

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