Algebraic structureof step nesting designs

Célia Fernandes; Paulo Ramos; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2010)

  • Volume: 30, Issue: 2, page 221-235
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Célia Fernandes, Paulo Ramos, and João Tiago Mexia. "Algebraic structureof step nesting designs." Discussiones Mathematicae Probability and Statistics 30.2 (2010): 221-235. <http://eudml.org/doc/277071>.

@article{CéliaFernandes2010,
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.},
author = {Célia Fernandes, Paulo Ramos, João Tiago Mexia},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {commutative Jordan algebras; cartesian product of commutative Jordan algebras; step nesting; variance components; UMVUE; Cartesian product of commutative Jordan algebras},
language = {eng},
number = {2},
pages = {221-235},
title = {Algebraic structureof step nesting designs},
url = {http://eudml.org/doc/277071},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Célia Fernandes
AU - Paulo Ramos
AU - João Tiago Mexia
TI - Algebraic structureof step nesting designs
JO - Discussiones Mathematicae Probability and Statistics
PY - 2010
VL - 30
IS - 2
SP - 221
EP - 235
AB - 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.
LA - eng
KW - commutative Jordan algebras; cartesian product of commutative Jordan algebras; step nesting; variance components; UMVUE; Cartesian product of commutative Jordan algebras
UR - http://eudml.org/doc/277071
ER -

References

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