DOI QR코드

DOI QR Code

Noninformative Priors for the Common Intraclass Correlation Coefficient

  • Kim, Dal-Ho (Department of Statistics, Kyungpook National University)
  • Received : 20110200
  • Accepted : 20110300
  • Published : 2011.03.31

Abstract

In this paper, we develop the noninformative priors for the common intraclass correlation coefficient when independent samples drawn from multivariate normal populations. We derive the first and second order matching priors. We reveal that the second order matching prior dose not match alternative coverage probabilities up to the second order and is not a HPD matching prior. It turns out that among all of the reference priors, one-at-a-time reference prior satisfies a second order matching criterion. Our simulation study indicates that one-at-a-time reference prior performs better than the other reference priors in terms of matching the target coverage probabilities in a frequentist sense.

Keywords

References

  1. Berger, J. O. and Bernardo, J. M. (1989). Estimating a product of means: Bayesian analysis with reference priors, Journal of the American Statistical Association, 84, 200–207.
  2. Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion), Bayesian Statistics IV, J. M. Bernardo, et. al., Oxford University Press, Oxford, 35–60.
  3. Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion), Journal of Royal Statistical Society, Series B, 41, 113–147.
  4. Cox, D. R. and Reid, N. (1987). Orthogonal parameters and approximate conditional inference (with discussion), Journal of Royal Statistical Society, Series B, 49, 1–39.
  5. Datta, G. S. and Ghosh, J. K. (1995a). On priors providing frequentist validity for Bayesian inference, Biometrika, 82, 37–45. https://doi.org/10.1093/biomet/82.1.37
  6. Datta, G. S. and Ghosh, M. (1995b). Some remarks on noninformative priors, Journal of the American Statistical Association, 90, 1357–1363.
  7. Datta, G. S. and Ghosh, M. (1996). On the invariance of noninformative priors, The Annal of Statistics, 24, 141–159.
  8. Datta, G. S., Ghosh, M. and Mukerjee, R. (2000). Some new results on probability matching priors, Calcutta Statistical Association Bulletin, 50, 179–192.
  9. DiCiccio, T. J. and Stern, S. E. (1994). Frequentist and Bayesian Bartlett correction of test statistics based on adjusted profile likelihood, Journal of Royal Statistical Society, Series B, 56, 397–408.
  10. Donner, A. and Bull, S. (1983). Inference concerning a common intraclass correlation coefficient, Biometrics, 39, 771–775.
  11. Ghosh, J. K. and Mukerjee, R. (1992). Noninformative priors (with discussion), Bayesian Statistics IV, J. M. Bernardo, et. al., Oxford University Press, Oxford, 195-210.
  12. Ghosh, J. K. and Mukerjee, R. (1995). Frequentist validity of highest posterior density regions in the presence of nuisance parameters, Statistics & Decisions, 13, 131–139.
  13. Huang, W. and Sinha, B. K. (1993). On optimum invariant tests of equality of intraclass correlation coefficents, Annals of the Institute of Statistical Mathematics, 45, 579–597. https://doi.org/10.1007/BF00773357
  14. Konishi, S. and Gupta, A. K. (1989). Testing the equality several intraclass correlation coefficients, Journal of Statistical Planning and Inference, 21, 93–105. https://doi.org/10.1016/0378-3758(89)90022-0
  15. Mukerjee, R. and Dey, D. K. (1993). Frequentist validity of posterior quantiles in the presence of a nuisance parameter: Higher order asymptotics, Biometrika, 80, 499–505.
  16. Mukerjee, R. and Ghosh, M. (1997). Second order probability matching priors, Biometrika, 84, 970–975.
  17. Mukerjee, R. and Reid, N. (1999). On a property of probability matching priors: Matching the alter-native coverage probabilities, Biometrika, 86, 333–340.
  18. Snedecor, G. W. and Cochran, G. (1980) Statistical Methods, 7th Ed., Iowa State University Press, Ames, Iowa.
  19. Stein, C. (1985). On the coverage probability of confidence sets based on a prior distribution, Sequential Methods in Statistics, Banach Center Publications, 16, 485–514.
  20. Tibshirani, R. (1989). Noninformative priors for one parameter of many, Biometrika, 76, 604–608.
  21. Welch, B. N. and Peers, B. (1963). On formulae for confidence points based on integrals of weighted likelihood, Journal of Royal Statistical Society, Series B, 25, 318–329
  22. Young, D. J. and Bhandary, M. (1998). Test for equality of intraclass correlation coefficients under unequal family sizes, Biometrics, 54, 1363–1373.