On Second Order Probability Matching Criterion in the One-Way Random Effect Model

  • Published : 2001.04.01

Abstract

In this paper, we consider the second order probability matching criterion for the ratio of the variance components under the one-way random effect model. It turns out that among all of the reference priors given in Ye(1994), the only one reference prior satisfies the second order matching criterion. Similar results are also obtained for the intraclass correlation as well.

Keywords

References

  1. Journal of the American Statistical Association v.84 Estimating a product of means:Bayesian analysis with reference priors Berger,J.O.;Bernardo,J.M.
  2. Bayesian Statistics Ⅳ On the development of reference priors(with discussion) Berger,J.O.;Bernardo,J.M.;J.M.Bernardo(et al.)
  3. Journal of Royal Statistical Society, B, v.41 Reference posterior distributions for Bayesian inference (with discussion) Bernardo,J.M.
  4. Bayesian Inference in Statistical Analysis Box,G.;Tiao,G.
  5. Communications in Statistics-Theory and Methods v.27 Bayesian approach to estimation of intraclass correlation using reference prior Chung,Y.;Dey,D.K.
  6. Journal of Royal Statistical Society, B, v.49 Orthogonal parameters and approximate conditional inference(with discussion) Cox,D.R.;Reid,N.
  7. Biometrika v.82 On priors providing frequentist validity for Bayesian inference Datta,G.S.;Ghosh,J.K.
  8. Journal of the American Statistical Association v.90 Some remarks on noninformative priors Datta,G.S.;Ghosh,M.
  9. The Annal of Statistics v.24 On the invariance of noninformative priors Datta,G.S.;Ghosh,M.
  10. Biometrics v.12 Confidence intervals for variance ratios specifying genetic heritability Graybill,F.A.;Martin,F.;Godfrey,G.
  11. Journal of the American Statistical Association v.60 Inference about variance components in the one-way model Hill,B.
  12. Biometrika v.80 Frequentist validity of posterior quantiles in the presence of a nuisance parameter:higher order asymptotics Mukerjee,R.;Dey,D.K.
  13. Biometrika v.84 Second order probability matching priors Mukerjee,R.;Ghosh,M.
  14. Communications in Statistics-Theory and Methods v.19 A comparision of Bayes and maximum likelihood estimation of the intraclass correlation coefficient Palmer,J.L.;Broemeling,L.D.
  15. Sequential Methods in Statistics v.16 On the coverage probability of confidence sets based on a prior distribution Stein,C.
  16. Biometrika v.86 Orthogonality and transformations in variance components models Solomon,P.J.;Taylor,J.M.G.
  17. Biometrika v.76 Noninformative Priors for One Parameter of Many Tibshirani,R.
  18. Journal of Statistical Planning and Inference v.41 Bayesian reference prior analysis on the ratio of variances for the balanced one-way random effect model Ye,K.
  19. Journal of Royal Statistical Society v.35 On formulae for confidence points based on integrals of weighted likelihood Welch,B.N.;Peers,B.