# Algebraic structure for the crossing of balanced and stair nested designs

Célia Fernandes; Paulo Ramos; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2014)

- Volume: 34, Issue: 1-2, page 71-88
- ISSN: 1509-9423

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topCélia Fernandes, Paulo Ramos, and João Tiago Mexia. "Algebraic structure for the crossing of balanced and stair nested designs." Discussiones Mathematicae Probability and Statistics 34.1-2 (2014): 71-88. <http://eudml.org/doc/271055>.

@article{CéliaFernandes2014,

abstract = {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.},

author = {Célia Fernandes, Paulo Ramos, João Tiago Mexia},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {balanced nested designs; stair nested designs; crossing; commutative Jordan algebras; variance components; inference},

language = {eng},

number = {1-2},

pages = {71-88},

title = {Algebraic structure for the crossing of balanced and stair nested designs},

url = {http://eudml.org/doc/271055},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Célia Fernandes

AU - Paulo Ramos

AU - João Tiago Mexia

TI - Algebraic structure for the crossing of balanced and stair nested designs

JO - Discussiones Mathematicae Probability and Statistics

PY - 2014

VL - 34

IS - 1-2

SP - 71

EP - 88

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/271055

ER -

## References

top- [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. Zbl1272.62051
- [2] C. Fernandes, P. Ramos and J. Mexia, Crossing balanced nested and stair nested designs, Electron. J. Linear Algebra 25 (2012) 22-47. Zbl1302.62178
- [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. Zbl1049.62065
- [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. Zbl1113.62004
- [5] A. Khuri, T. Mathew and B. Sinha, Statistical tests for mixed linear models (John Wiley and Sons, New York, 1998). Zbl0893.62009
- [6] N. Jacobson, Structure and Representation of Jordan Algebras (Colloqium Publications 39, American Mathematical Society, 1968). Zbl0218.17010
- [7] P. Jordan, J. von Neumann and E. Wigner, On a algebraic generalization of the quantum mechanical formulation, Ann. Math. 35 (1934) 9-64. Zbl60.0902.02
- [8] J. Seely, Linear spaces and unbiased estimation, Ann. Math. Stat. 41 (1970) 1725-1734. doi: 10.1214/aoms/1177696817. Zbl0263.62040
- [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. Zbl0263.62041
- [10] J. Seely, Quadratic subspaces and completeness, Ann. Math. Stat. 42 (1971) 710-721. doi: 10.1214/aoms/1177693420. Zbl0249.62067

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