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 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.

• Autores: Longford, Nicholas T.; Andrade, Mercedes
• Tipo de recurso: Article of journal
• Fecha de publicación: 2015
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• 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/
• 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.
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional