¹Universitat Pompeu Fabra, SNTL and Department of Economics and Business, Barcelona, Spain. Professor. Email: sntlnick@sntl.co.uk
²Universidad del Valle, School of Statistics, Cali, Colombia. Professor. Email: mercedes.andrade@correounivalle.edu.co

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 athletes training performance is presented.

Key words: Analysis of Variance with Random Effects, Decision, Equilibrium, Expected Loss, Variance Ratio.

La estimación de una de las varianzas en el modelo de análisis de la varianza con efectos aleatorios y la prueba de hipótesis de que la varianza se anula, son temas importantes en muchas aplicaciones. Tales inferencias están fuera de los confines de la teoría asintótica estándar porque una varianza cero está en la frontera del espacio paramétrico y la máxima verosimilitud u otro estimador razonable de una varianza tiene una probabilidad no trivial de cero en muchos contextos. Nosotros derivamos una regla de decisión sobre la razón de varianzas en un análisis de varianza de un factor balanceado tanto para la perspectiva frecuentista como la Bayesiana. Argumentamos que este enfoque es superior a la prueba de hipótesis porque incorpora las consecuencias de los dos tipos de error (elección incorrecta) que pueden cometerse. Se presenta una aplicación sobre los rendimientos de los entrenamientos de un atleta de pista.

Palabras clave: análisis de varianza con efectos aleatorios, decisión, equilibrio, pérdida esperada, razón de la varianza.

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