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Strictly associated models, prime basis factorials: an application

100%

Carvalho F.

Discussiones Mathematicae Probability and Statistics

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2011

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tom 31

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nr 1-2

77-86

EN

Mixed models will be considered using the Commutative Jordan Algebra of Symmetric matrices approach. Prime basis factorial models will now be considered in the framework provided by Commutative Jordan Algebra of Symmetric matrices. This will enable to obtain fractional replicates when the number of levels is neither a prime or a power of a prime. We present an application to the effect of lidocaine, at an enzymatic level, on the heart muscle of beagle dogs

2

Orthogonal models: Algebraic structure and explicit estimators for estimable vectors

88%

Pereira A., Fonseca M., Mexia J.

Discussiones Mathematicae Probability and Statistics

|

2015

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tom 35

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nr 1-2

29-44

EN

We study the algebraic structure of orthogonal models thus of mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known pairwise orthogonal projection matrices, POOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expression for the LSE of these models.

3

Algebraic structure for the crossing of balanced and stair nested designs

75%

Fernandes C., Ramos P., Mexia J.

Discussiones Mathematicae Probability and Statistics

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2014

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tom 34

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nr 1-2

71-88

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.

Ograniczanie wyników

3 Discussiones Mathematicae Probability and Statistics

2 Mexia J.

1 Carvalho F.

1 Fernandes C.

1 Fonseca M.

1 Pereira A.

1 Ramos P.

1 2015

1 2014

1 2011

Strictly associated models, prime basis factorials: an application

Orthogonal models: Algebraic structure and explicit estimators for estimable vectors

Algebraic structure for the crossing of balanced and stair nested designs