F-tests for generalized linear hypotheses in subnormal models

Joao Tiago Mexia; Gerberto Carvalho Dias

Discussiones Mathematicae Probability and Statistics (2001)

  • Volume: 21, Issue: 1, page 49-62
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Joao Tiago Mexia, and Gerberto Carvalho Dias. "F-tests for generalized linear hypotheses in subnormal models." Discussiones Mathematicae Probability and Statistics 21.1 (2001): 49-62. <http://eudml.org/doc/287649>.

@article{JoaoTiagoMexia2001,
abstract = {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.},
author = {Joao Tiago Mexia, Gerberto Carvalho Dias},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {F-tests; subnormal models; mixed models; invariance; UMP tests; third type error; unbiased most powerful},
language = {eng},
number = {1},
pages = {49-62},
title = {F-tests for generalized linear hypotheses in subnormal models},
url = {http://eudml.org/doc/287649},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Joao Tiago Mexia
AU - Gerberto Carvalho Dias
TI - F-tests for generalized linear hypotheses in subnormal models
JO - Discussiones Mathematicae Probability and Statistics
PY - 2001
VL - 21
IS - 1
SP - 49
EP - 62
AB - 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.
LA - eng
KW - F-tests; subnormal models; mixed models; invariance; UMP tests; third type error; unbiased most powerful
UR - http://eudml.org/doc/287649
ER -

References

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  9. [9] G.A.F. S, The Linear Hypothesis: a General Theory, 2nd (ed), Charles Griffin & Co. London 1980. 
  10. [10] M.J. S, Robust tests of inequality constraints and one-sided hypothesis in the linear model, Biometrika, Vol. 73, No 3, (1992). 
  11. [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. [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. [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). 

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