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...
| Authors: | , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10230/59371 |
| Online Access: | http://hdl.handle.net/10230/59371 http://dx.doi.org/10.15446/rce.v38n1.48810 |
| Access Level: | Open access |
| Keyword: | Analysis of variance with Random effects Decision Equilibrium Expected loss Variance ratio |
| Summary: | 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. |
|---|