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

Aníbal Areia; Francisco Carvalho; João T. Mexia

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 135-140, electronic only
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Aníbal Areia, Francisco Carvalho, and João T. Mexia. "Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models." Open Mathematics 13.1 (2015): 135-140, electronic only. <http://eudml.org/doc/268731>.

@article{AníbalAreia2015,
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.},
author = {Aníbal Areia, Francisco Carvalho, João T. Mexia},
journal = {Open Mathematics},
keywords = {Orthogonal models; Perfect families; Commutative Jordan algebras; orthogonal models; perfect families; commutative Jordan algebras},
language = {eng},
number = {1},
pages = {135-140, electronic only},
title = {Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models},
url = {http://eudml.org/doc/268731},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Aníbal Areia
AU - Francisco Carvalho
AU - João T. Mexia
TI - Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 135
EP - 140, electronic only
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.
LA - eng
KW - Orthogonal models; Perfect families; Commutative Jordan algebras; orthogonal models; perfect families; commutative Jordan algebras
UR - http://eudml.org/doc/268731
ER -

References

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  1. [1] Carvalho, Francisco; Mexia, João T.; Oliveira, M. Manuela, Estimation in Models with Commutative Orthogonal Block Structure, J. Stat. Theory Pract., 2009, 3 (2), 525-535 Zbl1211.62093
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