Discussiones Mathematicae Probability and Statistics 23(2) (2003) 167-174

SELECTIVE F TESTS FOR SUB-NORMAL MODELS

Célia Maria Pinto Nunes

Departamento de Matemática,Universidade da Beira Interior,
6200 Covilhã, Portugal

João Tiago Mexia

Universidade Nova de Lisboa, Departamento de Matemática
da Faculdade de Ciências e Tecnologia
Quinta da Torre, 2825-114 Monte de Caparica, Portugal
e-mail:
parcr@mail.fct.unl.pt

Abstract

F tests that are specially powerful for selected alternatives are built for sub-normal models. In these models the observation vector is the sum of a vector that stands for what is measured with a normal error vector, both vectors being independent. The results now presented generalize the treatment given by Dias (1994) for normal fixed-effects models, and consider the testing of hypothesis on the ordering of mean values and components.

Keywords: sective F tests, sub-normal models, max-min tests, orderings.

2000 Mathematics Subject Classification: 62J12, 62J99.

References

[1]J.T. Mexia, Controlled Heteroscedasticity, Quotient Vector Spaces and F Tests for Hypothesis on Mean Vectors, Trabalhos de Investigação, No. 1, FCT/UNL (1989).
[2]G.C. Dias, Selective F tests, Trabalhos de Investigação, No. 1. FCT/UNL (1994).
[3]C.M.P. Nunes and J.T. Mexia, Perturbations in Sub-normal Models, In Statistical Modelling- Proceedings of the 15th International Workshop on Statistical Modelling (V. Núñez-Antón, E. Ferreira, eds.), p. 485-488. Bilbao, Spain, July 17-21, (2000).
[4]J.T. Mexia and G.C. Dias, F Tests for generalized linear hypothesis in sub-normal models, Discussiones Mathematicae - Probability and Statistics, 21 (1) (2001), 49-62.

Received 15 April 2003