Inference for random effects in prime basis factorials using commutative Jordan algebras

• Autorzy: Vera M. Jesus , Paulo Canas Rodrigues , João Tiago Mexia
• Języki publikacji: EN

Abstrakty

EN

Commutative Jordan algebras are used to drive an highly tractable framework for balanced factorial designs with a prime number p of levels for their factors. Both fixed effects and random effects models are treated. Sufficient complete statistics are obtained and used to derive UMVUE for the relevant parameters. Confidence regions are obtained and it is shown how to use duality for hypothesis testing.

Słowa kluczowe

EN

prime basis factorial; commutative Jordan algebras; complete sufficient statistics; UMVUE; confidence regions

Kategorie tematyczne

• 62J15: Paired and multiple comparisons
• 62J12: Generalized linear models

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2007
• Tom: 27
• Numer: 1-2
• Strony: 15-25

Daty

wydano

2007

otrzymano

2006-12-20

poprawiono

2007-11-06

Twórcy

autor

Vera M. Jesus

• CMA-Center of Mathematics and Applications, Faculty of Science and Technology, Nova University of Lisbon, Monte de Caparica 2829-516 Caparica, Portugal

autor

Paulo Canas Rodrigues

• CMA-Center of Mathematics and Applications, Faculty of Science and Technology, Nova University of Lisbon, Monte de Caparica 2829-516 Caparica, Portugal

autor

João Tiago Mexia

• CMA-Center of Mathematics and Applications, Faculty of Science and Technology, Nova University of Lisbon, Monte de Caparica 2829-516 Caparica, Portugal

Bibliografia

• [1] A. Day and R. Mukerjee, Fractional Factorial Plans, Wiley Series in Probability and Statistics (1999).
• [2] 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.
• [3] J.T. Mexia, Standardized Orthogonal Matrices and the Decomposition of the sum of Squares for Treatments, Trabalhos de Investigação nº2, Departamento de Matemática, FCT-UNL (1988).
• [4] J.T. Mexia, Introdução à Inferência Estatística Linear, Edições Universitárias Lusófonas (1995).
• [5] J.R. Schoot, Matrix Analysis for Statistics, Wiley Interscience (1997).
• [6] J. Seely, Quadratic subspaces and completeness Ann. Math. Stat. (1971), 701-721.

Identyfikatory

DOI

10.7151/dmps.1086