# 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

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topCélia 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 -

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