Discussiones Mathematicae Probability and Statistics 24(2) (2004) 281-288

Selective Generalized F Tests

C. Nunes

Departamento de Matematica, Universidade da Beira Interior
Avenida Marques D'Avila e Bolama
6201-001 Covilha, Portugal

J.T. Mexia

Departamento de Matematica, Universidade Nova de Lisboa
Faculdade de Ciencias e Tecnologia
Quinta da Torre, 2825-114 Monte da Caparica, Portugal

Abstract

Generalized F tests were introduced by Michalski and Zmyślony (1996) for variance components and later (1999) for linear functions of parameters in mixed linear models. We now use generalized polar coordinates to obtain, for the second case, tests that are more powerful for selected families of alternatives.

Keywords: mixed linear models, variance components, generalized polar coordinates, selective F testes.

2000 Mathematics Subject Classification: 62J10, 62J12, 62J99.

References

[1] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310.
[2] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 17 (1999), 103-110.
[3] C. Nunes and J.T. Mexia, Selective F tests for sub-normal models, Discussiones Mathematicae, Probability and Statistics 23 (2003), 167-174.
[4] G. Dias, Selective F tests, Trabalhos de Investigação No 1, FCT/UNL (1994).
[5] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distribution for the generalized F tests, Discussiones Mathematicae, Probability and Statistics (1,2) 22 (2002), 37-51.
[6] M.G. Kendall, A Ccourse in the Geometry of n Dimensions, Charles Griffin & Company Limited, London 1961.

Received 1 June 2004