@inproceedings{71460d58260344bb977a31275db287eb,

title = "Inference with inducer pivot variables, an application to the one-way ANOVA",

abstract = "Having in mind complete and sufficient statistics for a relevant set of parameters of a given model, we show how to induce probability measures in the parameter spaces, which may be used to obtain confidence intervals. Hypothesis testing for these parameters can be carried out trough duality. Since the computations to construct induced measures tend to be heavy, we explain how they can be constructed through Monte-Carlo methods. We give the random effects linear model as an example, showing how to obtain complete sufficient statistics for such models from which UMVUE are obtained for the variance components. We derive explicit formulas for the One-Way ANOVA model.",

keywords = "Analysis of Variance, Hypothesis Testing, Inference, Linear Models, Measure Theory",

author = "Ricardo Covas and Mexia, {Jo{\~a}o Tiago} and C{\'e}lia Fernandes and Paulo Ramos",

year = "2011",

doi = "10.1063/1.3636921",

language = "English",

isbn = "9780735409569",

series = "AIP Conference Proceedings",

publisher = "AIP - American Institute of Physics",

pages = "1631--1634",

editor = "Simos, {Theodore E.} and George Psihoyias and Ch. Tsitouras and Zacharias Anastassi",

booktitle = "Numerical Analysis and Applied Mathematics",

address = "United States",

note = "International Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011 ; Conference date: 19-09-2011 Through 25-09-2011",

}