Decision theory for the variance ratio in ANOVA with random effects
N. T. Longford and M. Andrade Bejarano
Abstract
Estimating a variance component in a model of the analysis of variance
and testing the hypothesis that the variance vanishes
are important issues in many applications.
Such inferences are outside 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 a 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,
and argue that this approach is superior to hypothesis testing,
because it incorporates the consequences of the two kinds of error
(inappropriate choice) that can be made.
In Colombian Journal of Statistics (Revista Colombiana de Estadistica)
38, 181-207, 2015.