F-tests for generalized linear hypotheses in subnormal models

• Autorzy: Joao Tiago Mexia , Gerberto Carvalho Dias
• Języki publikacji: 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.

Słowa kluczowe

EN

F-tests; subnormal models; mixed models; invariance; UMP tests; third type error

Kategorie tematyczne

• 62J99: None of the above, but in this section
• 62J10: Analysis of variance and covariance

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 49-62

Daty

wydano

2001

otrzymano

2000-11-21

Twórcy

autor

Joao Tiago Mexia

• Departamento de Matemática, Universidade Nova de Lisboa, Faculdade de Ciencias e Tecnologia, Quinta da Torre, 2825 Monte da Caparica, Portugal

autor

Gerberto Carvalho Dias

• 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.
• [13] R.R. V, and J.T. M, Convergence of matrices and subspaces with statistical applications, Anais do Centro de Matemática e Aplicaçoes, I (2) (1995).

Identyfikatory

DOI

10.7151/dmps.1019