Algebraic structure for the crossing of balanced and stair nested designs

• Autorzy: Célia Fernandes , Paulo Ramos , João Tiago Mexia
• Języki publikacji: EN

Abstrakty

EN

Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.

Słowa kluczowe

EN

balanced nested designs; stair nested designs; crossing; commutative Jordan algebras; variance components; inference

Kategorie tematyczne

• 62J10: Analysis of variance and covariance

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2014
• Tom: 34
• Numer: 1-2
• Strony: 71-88

Daty

wydano

2014

otrzymano

2014-08-07

Twórcy

autor

Célia Fernandes

• ADM - Área Departamental de Matemática, ISEL - Instituto Superior de Engenharia de Lisboa, Lisboa, Portugal
• CMA - Centro de Matemática e Aplicações, FCT - Faculdade de Ciências e Tecnologia UNL - Universidade Nova de Lisboa, Caparica, Portugal

autor

Paulo Ramos

• ADM - Área Departamental de Matemática, ISEL - Instituto Superior de Engenharia de Lisboa, Lisboa, Portugal
• CMA - Centro de Matemática e Aplicações, FCT - Faculdade de Ciências e Tecnologia UNL - Universidade Nova de Lisboa, Caparica, Portugal

autor

João Tiago Mexia

• CMA - Centro de Matemática e Aplicações, FCT - Faculdade de Ciências e Tecnologia UNL - Universidade Nova de Lisboa, Caparica, Portugal

Bibliografia

• [1] C. Fernandes, P. Ramos and J. Mexia, Algebraic structure of step nesting designs, Discuss. Math. Probab. Stat. 30 (2010) 221-235. doi: 10.7151/dmps.1129.
• [2] C. Fernandes, P. Ramos and J. Mexia, Crossing balanced nested and stair nested designs, Electron. J. Linear Algebra 25 (2012) 22-47.
• [3] M. Fonseca, J. Mexia and R. Zmyślony, Estimators and tests for variance components in cross nested orthogonal designs, Discuss. Math. Probab. Stat. 23 (2003) 175-201.
• [4] M. Fonseca, J. Mexia and R. Zmyślony, Binary Operations on Jordan Algebras and Orthogonal Normal Models, Linear Algebra Appl. 417 (2006) 75-86. doi: 10.1016/j.laa.2006.03.045.
• [5] A. Khuri, T. Mathew and B. Sinha, Statistical tests for mixed linear models (John Wiley and Sons, New York, 1998).
• [6] N. Jacobson, Structure and Representation of Jordan Algebras (Colloqium Publications 39, American Mathematical Society, 1968).
• [7] P. Jordan, J. von Neumann and E. Wigner, On a algebraic generalization of the quantum mechanical formulation, Ann. Math. 35 (1934) 9-64.
• [8] J. Seely, Linear spaces and unbiased estimation, Ann. Math. Stat. 41 (1970) 1725-1734. doi: 10.1214/aoms/1177696817.
• [9] J. Seely, Linear spaces and unbiased estimators - Application to the mixed linear model, Ann. Math. Stat. 41 (1970) 1735-1745. doi: 10.1214/aoms/1177696818.
• [10] J. Seely, Quadratic subspaces and completeness, Ann. Math. Stat. 42 (1971) 710-721. doi: 10.1214/aoms/1177693420.

Identyfikatory

DOI

10.7151/dmps1162