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

Abstract

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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.

How to cite

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Célia 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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  1. [1] G. Dias, Selective F tests, Trabalhos de Investigação, N°1. FCT/UNL (1994). Zbl0834.62050
  2. [2] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distribution for the generalized F tests, Discussiones Mathematicae, Probability and Statistics 22 (1,2) (2002), 37-51. Zbl1037.62004
  3. [3] M. Fonseca, J.T. Mexia and R. Zmyślony, Estimators and Tests for Variance Components in Cross Nested Orthogonal Designs, Discussions Mathematicae, Probability and Statistics 23 (2003), 175-201. Zbl1049.62065
  4. [4] J.T. Mexia, Best linear unbiased estimates, duality of F tests and the Scheffé multiple comparison method in presence of controled heterocedasticity, Comp. Statist. & Data Analysis 10 (3) (1990). Zbl0825.62484
  5. [5] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310. Zbl0842.62059
  6. [6] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 17 (1999), 103-110. Zbl0987.62012
  7. [7] C. Nunes and J.T. Mexia, Selective generalized F tests, Discussiones Mathematicae, Probability and Statistics 24 (2004), 281-288. Zbl1165.62306
  8. [8] C. Nunes and J.T. Mexia, Non-central generalized F distributions, Discussiones Mathematicae, Probability and Statistics 26 (2006), 47-61. Zbl1128.62018
  9. [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
  10. [10] J.R. Schott, Matrix Analysis for Statistics, Jonh Wiley & Sons, New York 1997. Zbl0872.15002
  11. [11] J. Seely, Quadratic subspaces and completeness, The Annals of Mathematical Statistics 42 (2) (1971), 710-721. Zbl0249.62067

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