Skip to main content
SpringerLink
Log in

Noninformative priors for linear combinations of the normal means

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

In this paper, we develop noninformative priors for linear combinations of the means under the normal populations. It turns out that among the reference priors the one-at-a-time reference prior satisfies a second order probability matching criterion. Moreover, the second order probability matching priors match alternative coverage probabilities up to the second order and are also HPD matching priors. Our simulation study indicates that the 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Google Scholar 

  3. Bernardo, J.M. (1979). Reference Posterior Distributions for Bayesian Inference (with discussion). Journal of Royal Statistical Society, B, 41, 113–147.

    MATH  MathSciNet  Google Scholar 

  4. Cox, D.R. and Reid, N. (1987). Orthogonal Parameters and Approximate Conditional Inference (with discussion). Journal of Royal Statistical Society, B, 49, 1–39.

    MATH  MathSciNet  Google Scholar 

  5. Datta, G.S. and Ghosh, J.K. (1995). On Priors Providing Frequentist Validity for Bayesian Inference. Biometrika, 82, 37–45.

    Article  MATH  MathSciNet  Google Scholar 

  6. Datta, G.S. and Ghosh, M. (1995). Some Remarks on Noninformative Priors. Journal of the American Statistical Association, 90, 1357–1363.

    Article  MATH  MathSciNet  Google Scholar 

  7. Datta, G.S. and Ghosh, M. (1996). On the Invariance of Noninformative Priors. The Annal of Statistics, 24, 141–159.

    Article  MATH  MathSciNet  Google Scholar 

  8. Datta, G.S., Ghosh, M. and Mukerjee, R. (2000). Some New Results on Probability Matching Priors. Calcutta Statistical Association Bulletin, 50, 179–192.

    MATH  MathSciNet  Google Scholar 

  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, B, 56, 397–408.

    MATH  MathSciNet  Google Scholar 

  10. 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.

    MATH  MathSciNet  Google Scholar 

  11. Hayter, A.J., Tetsuhisa Miwa and Wei Liu (2000). Combining the Advantages of One-sided and Two-sided Procedures for Comparing Several Treatments with a Control. Journal of Statistical Planning and Inference, 86, 81–99.

    Article  MATH  MathSciNet  Google Scholar 

  12. Hochberg, Y. and Tamhane, A.C. (1987). Multiple Comparisons Procedures. Wiley, New York.

    Google Scholar 

  13. Li, H. and Stern, H.S. (1997). Bayesian Inference for Nested Designs Based on Jeffreys's Prior. The American Statistician, 51, 219–224.

    Article  MathSciNet  Google Scholar 

  14. 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.

    Article  MATH  MathSciNet  Google Scholar 

  15. Mukerjee, R. and Ghosh, M. (1997). Second Order Probability Matching Priors. Biometrika, 84, 970–975.

    Article  MATH  MathSciNet  Google Scholar 

  16. Mukerjee, R. and Reid, N. (1999). On A Property of Probability Matching Priors: Matching the Alternative Coverage Probabilities. Biometrika, 86, 333–340.

    Article  MATH  MathSciNet  Google Scholar 

  17. Steel, R.G.D. and Torrie, J.H. (1980). Principles and Procedures of Statistics: A Biometrical Approach (2/e) McGraw-Hill, New York.

    Google Scholar 

  18. 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.

  19. Tibshirani, R. (1989). Noninformative Priors for One Parameter of Many. Biometrika, 76, 604–608.

    Article  MATH  MathSciNet  Google Scholar 

  20. Welch, B.L. and Peers, H.W. (1963). On Formulae for Confidence Points based on Integrals of Weighted Likelihood. Journal of Royal Statistical Society, B, 25, 318–329.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Kyungpook National University, 702-701, Daegu, Korea

    Dal Ho Kim

  2. Department of Applied Statistics, Sangji University, 220-702, Wonju, Korea

    Sang Gil Kang

  3. Faculty of Information Science, Daegu Haany University, 712-230, Kyungsan, Korea

    Woo Dong Lee

Authors
  1. Dal Ho Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sang Gil Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Woo Dong Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, D.H., Kang, S.G. & Lee, W.D. Noninformative priors for linear combinations of the normal means. Statistical Papers 47, 249–262 (2006). https://doi.org/10.1007/s00362-005-0286-3

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-005-0286-3

Key words

Search

Navigation