Joint estimation for normal orthogonal mixed models

Vera de Jesus; Sandra Saraiva Ferreira; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2007)

  • Volume: 27, Issue: 1-2, page 5-13
  • ISSN: 1509-9423

Abstract

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Commutative Jordan algebras are used to express the structure of mixed orthogonal models and to derive complete sufficient statistics. From these statistics, UMVUE, (Uniformly Minimum Variance Unbiased Estimators), are derived for the relevant parameters, first of single models then of several such models. These models may correspond to experiments designed separately so our results may be seen as a contribution to this meta-analysis.

How to cite

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Vera de Jesus, Sandra Saraiva Ferreira, and João Tiago Mexia. "Joint estimation for normal orthogonal mixed models." Discussiones Mathematicae Probability and Statistics 27.1-2 (2007): 5-13. <http://eudml.org/doc/277022>.

@article{VeradeJesus2007,
abstract = {Commutative Jordan algebras are used to express the structure of mixed orthogonal models and to derive complete sufficient statistics. From these statistics, UMVUE, (Uniformly Minimum Variance Unbiased Estimators), are derived for the relevant parameters, first of single models then of several such models. These models may correspond to experiments designed separately so our results may be seen as a contribution to this meta-analysis.},
author = {Vera de Jesus, Sandra Saraiva Ferreira, João Tiago Mexia},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {normal orthogonal mixed models; commutative Jordan algebras; meta-analysis},
language = {eng},
number = {1-2},
pages = {5-13},
title = {Joint estimation for normal orthogonal mixed models},
url = {http://eudml.org/doc/277022},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Vera de Jesus
AU - Sandra Saraiva Ferreira
AU - João Tiago Mexia
TI - Joint estimation for normal orthogonal mixed models
JO - Discussiones Mathematicae Probability and Statistics
PY - 2007
VL - 27
IS - 1-2
SP - 5
EP - 13
AB - Commutative Jordan algebras are used to express the structure of mixed orthogonal models and to derive complete sufficient statistics. From these statistics, UMVUE, (Uniformly Minimum Variance Unbiased Estimators), are derived for the relevant parameters, first of single models then of several such models. These models may correspond to experiments designed separately so our results may be seen as a contribution to this meta-analysis.
LA - eng
KW - normal orthogonal mixed models; commutative Jordan algebras; meta-analysis
UR - http://eudml.org/doc/277022
ER -

References

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  1. [1] M. Fonseca, J.T. Mexia and R. Zmyślony, Binary operations on Jordan algebras and orthogonal normal models, Linear Algebra and its Applications 417 (2006), 75-86. Zbl1113.62004
  2. [2] D.A.S. Frazer, Nonparametric methods in statistics, Jonh Wiley & Sons - New York 1957. 
  3. [3] S.S. Ferreira, Inference for orthogonal models with segregation, PhD Thesis, UBI - Covilhă 2006. 
  4. [4] J. Seely, Quadratic subspaces and completeness, The Annals of Mathematical Statistics 42 (2) (1971), 710-721. Zbl0249.62067
  5. [5] J. Seely, Minimal sufficient statistics and completeness for multivariate normal families, Sankhya 39 (1977), 170-185. Zbl0409.62004

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