# Generalized F tests and selective generalized F tests for orthogonal and associated mixed models

Célia Nunes; Iola Pinto; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2008)

- Volume: 28, Issue: 2, page 229-246
- ISSN: 1509-9423

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topCélia Nunes, Iola Pinto, and João Tiago Mexia. "Generalized F tests and selective generalized F tests for orthogonal and associated mixed models." Discussiones Mathematicae Probability and Statistics 28.2 (2008): 229-246. <http://eudml.org/doc/277020>.

@article{CéliaNunes2008,

abstract = {The statistics of generalized F tests are quotients of linear combinations of independent chi-squares. Given a parameter, θ, for which we have a quadratic unbiased estimator, θ̃, the test statistic, for the hypothesis of nullity of that parameter, is the quotient of the positive part by the negative part of such estimator. Using generalized polar coordinates it is possible to obtain selective generalized F tests which are especially powerful for selected families of alternatives. We build both classes of tests for the orthogonal and associated mixed models. The associated models are obtained adding terms to the orthogonal models.},

author = {Célia Nunes, Iola Pinto, João Tiago Mexia},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {selective generalized F tests; generalized polar coordinates; associated models; selective generalized tests},

language = {eng},

number = {2},

pages = {229-246},

title = {Generalized F tests and selective generalized F tests for orthogonal and associated mixed models},

url = {http://eudml.org/doc/277020},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Célia Nunes

AU - Iola Pinto

AU - João Tiago Mexia

TI - Generalized F tests and selective generalized F tests for orthogonal and associated mixed models

JO - Discussiones Mathematicae Probability and Statistics

PY - 2008

VL - 28

IS - 2

SP - 229

EP - 246

AB - The statistics of generalized F tests are quotients of linear combinations of independent chi-squares. Given a parameter, θ, for which we have a quadratic unbiased estimator, θ̃, the test statistic, for the hypothesis of nullity of that parameter, is the quotient of the positive part by the negative part of such estimator. Using generalized polar coordinates it is possible to obtain selective generalized F tests which are especially powerful for selected families of alternatives. We build both classes of tests for the orthogonal and associated mixed models. The associated models are obtained adding terms to the orthogonal models.

LA - eng

KW - selective generalized F tests; generalized polar coordinates; associated models; selective generalized tests

UR - http://eudml.org/doc/277020

ER -

## References

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- [8] C. Nunes and J.T. Mexia, Non-central generalized F distributions, Discussiones Mathematicae, Probability and Statistics 26 (2006), 47-61. Zbl1128.62018
- [9] C. Nunes, I. Pinto and J.T. Mexia, F and selective F tests with balanced cross-nesting and associated models, Discussiones Mathematicae, Probability and Statistics 26 (2006), 193-205. Zbl1128.62080
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