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ArticleOriginal scientific text

Title

Algebraic structureof step nesting designs

Authors 1, 1, 2

Affiliations

  1. Área Científica de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 01 1959-007 Lisboa, Portugal
  2. Departamento de Matemática, Faculdade de Cięncias e Tecnologia Universidade Nova de Lisboa, Monte de Caparica 2829-516 Caparica, Portugal

Abstract

Step nesting designs may be very useful since they require fewer observations than the usual balanced nesting models. The number of treatments in balanced nesting design is the product of the number of levels in each factor. This number may be too large. As an alternative, in step nesting designs the number of treatments is the sum of the factor levels. Thus these models lead to a great economy and it is easy to carry out inference. To study the algebraic structure of step nesting designs we introduce the cartesian product of commutative Jordan algebras.

Keywords

ENG
commutative Jordan algebras, cartesian product of commutative Jordan algebras, step nesting, variance components, UMVUE

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Discussiones Mathematicae Probability and Statistics
2010/30/2
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Pages:
221-235
Main language of publication
English
Received
2010-02-05
Published
2010

DOI: 10.7151/dmps.1129

Exact and natural sciences