Discussiones Mathematicae Probability and Statistics 21(1) (2001) 49-62

Joao Tiago Mexia and Gerberto Carvalho Dias

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

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.

**Keywords:** F-tests, subnormal models, mixed models, invariance, UMP
tests, third type error.

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

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Received 21 November 2000