Discussiones Mathematicae Probability and Statistics 23(2) (2003) 175-201


Miguel Fonseca, João Tiago Mexia

Department of Mathematics, Faculty of Science and Technology
New University of Lisbon
Monte da Caparica 2829-516 Caparica, Portugal

Roman Zmyślony

Institute of Mathematics, University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland


Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.

Keywords: hypothesis testing, generalized F distribution, adaptative test, nested orthogonal designs.

2000 Mathematics Subject Classification: 62H10, 62H15, 62J10.


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Received 17 October 2003
Revised 17 December 2003