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- Title
UNIFIED THEORY OF TESTING HYPOTHESES IN MIXED LINEAR MODELS.
- Authors
MICHALSKI, ANDRZEJ
- Abstract
In the paper an effective method of testing hypotheses for fixed effects and variance components in mixed linear normal models is presented. A new idea in the problem of testing hypotheses for parameters in mixed linear models was born in the construction of test for vanishing of single variance component (Michalski and Zmyślony, 1996) [9]. This test has been based on the decomposition of quadratic form of the locally best quadratic unbiased estimator of this components. The F-ratio test rejects null hypothesis if the ratio of positive and negative part of the corresponding estimator is sufficiently large. Although the construction of this exact test requires quite strong assumptions (covariance matrices commute after using the usual invariance procedure with respect to the group of translations), for many classic models, analysis of variance and regression models, we can successfully apply this idea to get the classical tests for testing hypotheses about the parameters of the corresponding model, often with larger values of the power function. In the case of testing the fixed effects is sufficient to replace linear hypothesis by the equivalent square hypothesis. Next, we consider the respective functions of the model parameters, which are squarely estimable connected with the null hypothesis. This article is a review of the most important results obtained by Michalski and Zmyślony (1996 [9], 1999 [10]) and by Gąsiorek et al. (2000) [2] using this idea.
- Subjects
LINEAR statistical models; QUADRATIC forms; COVARIANCE matrices; F-test (Mathematical statistics); REGRESSION analysis
- Publication
Discussiones Mathematicae: Probability & Statistics, 2017, Vol 37, Issue 1/2, p123
- ISSN
1509-9423
- Publication type
Article
- DOI
10.7151/dmps.1191