Decision Theory for the Variance Ratio in One-Way ANOVA with Random Effects
Estimating a variance component in the model of analysis of variance with random effects and testing the hypothesis that the variance vanishes are important issues in many applications. Such inferences are beyond the confines of the standard (asymptotic) theory because a zero variance is on the boun...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/66548 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/66548 http://bdigital.unal.edu.co/67576/ |
| Access Level: | acceso abierto |
| Palabra clave: | 51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics Analysis of Variance with Random Effects Decision Equilibrium Expected Loss Variance Ratio Análisis de varianza con efectos aleatorios Decisión Equilibrio Pérdida esperada Tazón de la varianza. |
| Sumario: | Estimating a variance component in the model of analysis of variance with random effects and testing the hypothesis that the variance vanishes are important issues in many applications. Such inferences are beyond the confines of the standard (asymptotic) theory because a zero variance is on the boundary of the parameter space and the maximum likelihood or another reasonable estimator of variance has a non-trivial probability of zero in many settings. We derive decision rules regarding the variance ratio in balanced one-way analysis of variance, in both the frequentist and Bayesian perspectives. We argue that this approach is superior to hypothesis testing because it incorporates the consequences of the two kinds of error (incorrect choice) that may be committed. An application to a track athlete’s training performance is presented. |
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