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Tytuł artykułu

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

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EN
Abstrakty
EN
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.
Twórcy
autor
  • Mathematics Department, University of Beira Interior Covilhã, Portugal
autor
  • Superior Institute of Engineer of Lisbon Scientific Area of Mathematics, Lisboa, Portugal
  • Department of Mathematics, Faculty of Science and Technology New, New University of Lisbon, Monte da Caparica, Portugal
Bibliografia
  • [1] G. Dias, Selective F tests, Trabalhos de Investigação, N°1. FCT/UNL (1994).
  • [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.
  • [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.
  • [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).
  • [5] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310.
  • [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.
  • [7] C. Nunes and J.T. Mexia, Selective generalized F tests, Discussiones Mathematicae, Probability and Statistics 24 (2004), 281-288.
  • [8] C. Nunes and J.T. Mexia, Non-central generalized F distributions, Discussiones Mathematicae, Probability and Statistics 26 (2006), 47-61.
  • [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.
  • [10] J.R. Schott, Matrix Analysis for Statistics, Jonh Wiley & Sons, New York 1997.
  • [11] J. Seely, Quadratic subspaces and completeness, The Annals of Mathematical Statistics 42 (2) (1971), 710-721.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1102
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