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2001 | 21 | 1 | 49-62
Tytuł artykułu

F-tests for generalized linear hypotheses in subnormal models

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EN
Abstrakty
EN
When the measurement errors may be assumed to be normal and independent from what is measured a subnormal model may be used. We define a linear and generalized linear hypotheses for these models, and derive F-tests for them. These tests are shown to be UMP for linear hypotheses as well as strictly unbiased and strongly consistent for these hypotheses. It is also shown that the F-tests are invariant for regular transformations, possess structural stability and are almost strongly consistent for generalized linear hypothesis. An application to a mixed model studied by Michalskyi and Zmyślony is shown.
Twórcy
  • Departamento de Matemática, Universidade Nova de Lisboa, Faculdade de Ciencias e Tecnologia, Quinta da Torre, 2825 Monte da Caparica, Portugal
  • Departamento de Matemática, Universidade Nova de Lisboa, Faculdade de Ciencias e Tecnologia, Quinta da Torre, 2825 Monte da Caparica, Portugal
Bibliografia
  • [1] D.B. A and J.B. B, Influence curve of an F-tests based on robustweights, American Statistical Association, Proceedings of the Statistical Computing Section, Alexandria 1992.
  • [2] M. Fisz, Probability Theory and Mathematical Statistics, John Wiley & Sons, 3rd Edition New York 1963.
  • [3] E.L. L, Testing Statistical Hypothesis, John Wiley & Sons, New York 1959.
  • [4] J.T. M, Controlled Heterocedasticity, Quotient Vector Spaces and F-tests for Hypothesis on Mean Vectors, Trabalhos de Investigaçao, FCT/UNL,Lisbon 1989.
  • [5] A. M and R. Z, Testing Hypothesis for Linear Functions of Parameters in Mixed Linear Models, Tatra Mt. Math. Publ. 17 (1999), 103-110.
  • [6] J.N. Rao, B. S, and K. Yue, Generalized least squares F-tests in Regression Analysis with two-stage cluster samples, JASA. Vol. 88, No 424, (1993).
  • [7] C.R. Rao, Advanced Methods on Biometric Research, John Wiley & Sons New York 1952.
  • [8] H. S, The Analysis of Variance, John Wiley & Sons. New York 1959.
  • [9] G.A.F. S, The Linear Hypothesis: a General Theory, 2nd (ed), Charles Griffin & Co. London 1980.
  • [10] M.J. S, Robust tests of inequality constraints and one-sided hypothesis in the linear model, Biometrika, Vol. 73, No 3, (1992).
  • [11] J. T de O, Statistical Choice of Univariate Extreme Models, Statistical Distributions in Scientific Works, C. Tuillie et al. (eds), Reiche, Dordrécht, Vol. 6 (1980), 367-382.
  • [12] J. T de O, Decision and Modelling in Extremes, Some Recent Advances in Statistics, J. Tiago de Oliveira & B. Epstein (eds), Academic Press, New York (1982), 101-110.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1019
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