A modified harmonic mean test procedure for variance components |
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| Affiliation: | 1. Department of Statistics, UAE University, P.O. Box 17555 Al-Ain, UAEUnited Arab Emirates;2. Department of Statistics, Oregon State University, Corvallis, OR 97331-4606, USA;1. College of Construction Engineering, Jilin University, Changchun 130026, China;2. North China Institute of Science & Technology, Langfang 065201, China;3. Department of Geology, University of Cincinnati, Cincinnati, OH, USA;4. Departments of Environmental Engineering, University of Cincinnati, Cincinnati, OH, USA;5. Engineering Research Center of Geothermal Resources Development Technology and Equipment, Ministry of Education, Jilin University, Changchun, China;6. Earth and Environmental Sciences Department, Wright State University, Dayton, OH, USA;7. Department of Electrical Engineering and Energy Technology, University of Vaasa, P.O.Box 700, FIN-65101 Vaasa, Finland;1. Department of Mathematical Sciences, University of Texas at Dallas, 758080, Richardson, TX, USA;2. Fachbereich Mathematik, Universität Salzburg, A-5020, Austria;3. Department of Statistics, University of Kentucky, 40536, Lexington, KY, USA;4. Institute of Statistics, University of Ulm, Helmholtzstr. 20, 89081 Ulm, Germany |
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| Abstract: | A complete class of tests of variance components is characterized within the class of tests statistics of the form of a ratio of a linear combination of chi-squared random variables to an independent chi-squared random variable. This result is used in the context of general unbalanced mixed models to show that the harmonic mean method results in an inadmissible test of the random treatment effects. The harmonic mean procedure is then modified in such a way that the modified test uniformly dominates the original test. Two competitive tests are the LMP (locally most powerful) and Wald's tests, which have optimal power properties against small and large alternatives, respectively. A Monte Carlo simulation study reveals that the modified test outperforms both the LMP and Wald's tests in badly unbalanced designs and that it is a viable alternative in less unbalanced designs. |
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