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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationNumerical Analysis and Applied Mathematics
Subtitle of host publicationICNAAM 2011 - International Conference on Numerical Analysis and Applied Mathematics
EditorsTheodore E. Simos, George Psihoyias, Ch. Tsitouras, Zacharias Anastassi
Place of PublicationMelville
PublisherAmerican Institute of Physics
Pages1631-1634
Number of pages4
ISBN (Print)9780735409569
DOIs
Publication statusPublished - 2011
EventInternational Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011 - Halkidiki, Greece
Duration: 19 Sep 201125 Sep 2011

Publication series

NameAIP Conference Proceedings
Volume1389
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011
CountryGreece
CityHalkidiki
Period19/09/1125/09/11

Keywords

  • Analysis of Variance
  • Hypothesis Testing
  • Inference
  • Linear Models
  • Measure Theory

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