Discussiones Mathematicae Probability and Statistics 25(2) (2005) 241-249

STABLE HYPOTHESIS FOR MIXED MODELS WITH BALANCED CROSS-NESTING

Dário Ferreira1, João Tiago Mexia2 and Sandra Saraiva Ferreira1

1Department of Mathematics, University of Beira Interior
6200 Covilha, Portugal

2Department of Mathematics, Faculty of Science and Tecnology,
New University of Lisbon
Monte da Caparica, Portugal

email: sandraf@ubi.pt
email: dario@ubi.pt

Abstract

Stable hypothesis are hypothesis that may refer either for the fixed part or for the random part of the model. We will consider such hypothesis for models with balanced cross-nesting. Generalized F tests will be derived. It will be shown how to use Monte-Carlo methods to evaluate p-values for those tests.

Keywords: generalized F tests; mixed balanced models; cross-nesting.

2000 Mathematics Subject Classification: 62K15.

References

[1] M. Fonseca, J.T. Mexia and R. Zmyślony, Jordan Alebras, Generating Pivot variables and Orthogonal Mixed Models 22 (2004), 37-51.
[2] A. Michalski and R. Zmyślony, Testing Hypothesis For Variance Components in Mixed Linear Models, Statistics 27 (1996), 297-310.
[3] A. Michalski and R. Zmyślony, Testing Hypothesis For Linear Functions of Parameters in Mixed Linear Models, Tatra Mt Math Publications 17 (1999), 103-110.
[4] S. Weerahandi, Exact Statistical methods for Data Analysis, 2nd print. Springer Verlags 1996.
[5] S. Saraiva and J.T. Mexia, Alternative Analysis of an Experiment On Grapevines, Colloquium Biometryczne 34a (2004), 89-95.

Received 3 March 2005