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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1085,
author = {Vera de Jesus and Sandra Saraiva Ferreira and Jo\~ao Tiago Mexia},
title = {Joint estimation for normal orthogonal mixed models},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {27},
year = {2007},
pages = {5-13},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1085}
}
Vera de Jesus; Sandra Saraiva Ferreira; João Tiago Mexia. Joint estimation for normal orthogonal mixed models. Discussiones Mathematicae Probability and Statistics, Tome 27 (2007) pp. 5-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1085/
[000] [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. | Zbl 1113.62004
[001] [2] D.A.S. Frazer, Nonparametric methods in statistics, Jonh Wiley & Sons - New York 1957.
[002] [3] S.S. Ferreira, Inference for orthogonal models with segregation, PhD Thesis, UBI - Covilhă 2006.
[003] [4] J. Seely, Quadratic subspaces and completeness, The Annals of Mathematical Statistics 42 (2) (1971), 710-721. | Zbl 0249.62067
[004] [5] J. Seely, Minimal sufficient statistics and completeness for multivariate normal families, Sankhya 39 (1977), 170-185. | Zbl 0409.62004