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2015 | 13 | 1 |
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
wydano
2015-01-01
otrzymano
2013-12-09
zaakceptowano
2014-04-03
online
2014-10-28
Twórcy
  • Departamento de Economia e Gestão, Instituto Politécnico de Setúbal, 2910-761 Setúbal, Portugal
  • CMA – Centro de Matemática e Aplicações, Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia, 2829-516 Caparica, Portugal and Unidade Departamental de Matemática e Física, Instituto Politécnico de Tomar, 2300-313 Tomar, Portugal, fpcarvalho@ipt.pt
  • CMA – Centro de Matemática e Aplicações, Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia, 2829-516 Caparica, Portugal
Bibliografia
  • [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
  • [2] Drygas, H., Sufficiency and Completeness in the General Gauss-Markov Model, Sankhy¯ a, 1983, 45 (1), 88-89
  • [3] Ferreira, S.S.; Ferreira, D.; Fernandes, C.; Mexia, João T., Orthogonal models and perfect families of symmetric matrices, Bulletin of the ISI, Proceedings of ISI (22-28 August 2007, Lisbon, Portugal), Lisbon, 2007, 3252-3254
  • [4] Fonseca, M; Mexia, João T.; Zmy´slony, R., Binary operations on Jordan algebras and orthogonal normal models, Linear Algebra Appl., 2006, 417, 75-86
  • [5] Jordan, P.; von Neumann, J. and Wigner, E., On the algebraic generalization of the quantum mechanical formalism, Ann. of Math., 1934, 36, 26-64
  • [6] Lehmann, E.L. and Casella, G., Theory of Point Estimation, 2nd ed., Springer, 1998
  • [7] Schott, James R., Matrix Analysis for Statistics, Wiley Series in Probability and Statistics, 1997
  • [8] Seely, J., Linear spaces and unbiased estimators, Ann. Math. Stat., 1970a, 41, 1735-1745[Crossref]
  • [9] Seely, J., Linear spaces and unbiased estimators. Application to a mixed linear model, Ann. Math. Stat., 1970b, 41, 1735-1745[Crossref]
  • [10] Seely, J., Quadratic subspaces and completeness, Ann. Math. Stat., 1971a, 42, 710-721[Crossref]
  • [11] Seely, J., Zyskind, Linear spaces and minimum variance estimators, Ann. Math. Stat., 1971b, 42, 691-703[Crossref]
  • [12] Seely, J., Minimal sufficient statistics and completeness for multivariate normal families, Sankhy¯ a, 1977, 39 (2), 170-185
  • [13] VanLeeuwen, Dawn M.; Seely, Justus F.; Birkes, David S., Sufficient conditions for orthogonal designs in mixed linear models, J. Statist. Plann. Inference, 1998, 73, 373-389
  • [14] VanLeeuwen, Dawn M.; Birkes, David S.; Seely, Justus F., Balance and Orthogonality in Designs for Mixed Classification Models, Ann. Statist., 1999, 27 (6), 1927-1947
  • [15] Zmy´slony, R; Drygas, H., Jordan Algebras and Bayesian Quadratic Estimation of Variance Components, Linear Algebra Appl., 1992, 168, 259-275
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0009
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