Objective Bayesian hypothesis testing and estimation for the intraclass model

Duo Zhang, Daojiang He, Xiaoqian Sun, Tao Lu, Min Wang

Research output: Contribution to journalArticle

Abstract

The intraclass correlation coefficient (ICC) plays an important role in various fields of study as a coefficient of reliability. In this paper, we consider objective Bayesian analysis for the ICC in the context of normal linear regression model. We first derive two objective priors for the unknown parameters and show that both result in proper posterior distributions. Within a Bayesian decision-theoretic framework, we then propose an objective Bayesian solution to the problems of hypothesis testing and point estimation of the ICC based on a combined use of the intrinsic discrepancy loss function and objective priors. The proposed solution has an appealing invariance property under one-to-one reparametrisation of the quantity of interest. Simulation studies are conducted to investigate the performance the proposed solution. Finally, a real data application is provided for illustrative purposes.

Original languageEnglish
Pages (from-to)37-47
Number of pages11
JournalStatistical Theory and Related Fields
Volume2
Issue number1
DOIs
StatePublished - Jan 2 2018

Keywords

  • Bayesian reference criterion
  • Intraclass correlation coefficient
  • hypothesis testing
  • intrinsic discrepancy
  • intrinsic estimator
  • reference priors

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