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

ESTIMATORS AND TESTS FOR VARIANCE COMPONENTS IN CROSS NESTED ORTHOGONAL DESIGNS

Miguel Fonseca, João Tiago Mexia

Department of Mathematics, Faculty of Science and Technology
New University of Lisbon
Monte da Caparica 2829-516 Caparica, Portugal
e-mail:
fonsecamig@yahoo.com

Roman Zmyślony

Institute of Mathematics, University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland
e-mail:
r.zmyslony@im.uz.zgora.pl

Abstract

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