Conditional properties of Bayesian interval estimates

  • Anna Nicolaou
Bayesian Approach
  • 38 Downloads

Abstract

Consider the construction of an interval estimate for a scalar parameter of interest in the presence of orthogonal nuisance parameters. A conditional prior density on the parameter of interest that is proportional to the square root of its information element, generates one-sided Bayes intervals that are approximately confidence intervals as well, having coverage error of orderO(1/n), wheren is the sample size. We show that the frequency property of these intervals also holds conditionally on a locally ancillary statistic near the true parameter value.

Key words and phrases

Bayes intervals nuisance parameters orthogonal parameters local ancillarity 

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References

  1. Barndorff-Nielsen, O. E. (1986). Inference on full or partial parameters based on the standardized signed log likelihood ratio,Biometrika,73, 307–322.Google Scholar
  2. Barndorff-Nielsen, O. E. (1991). Modified signed log likelihood ratio,Biometrika,78, 557–563.Google Scholar
  3. Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion),J. Roy. Statist. Soc. Ser. B,41, 113–147.Google Scholar
  4. Cox, D. R. (1980). Local ancillarity,Biometrika,67, 279–286.Google Scholar
  5. Cox, D. R. and Reid, R. (1987). Orthogonal parameters and approximate conditional inference (with discussion),J. Roy. Statist. Soc. Ser. B,49, 1–39.Google Scholar
  6. DeBruijn, N. C. (1981).Asymptotic Methods in Analysis, Dover, New York.Google Scholar
  7. Ghosh, J. K. and Mukerjee, R. (1992). Bayesian and frequentist Bartlett corrections for likelihood ratio and conditional likelihood ratio tests,J. Roy. Statist. Soc. Ser. B,54, 867–875.Google Scholar
  8. Johnson, R. A. (1970). An asymptotic expansion for posterior distributions,Ann. Math. Statist.,38, 1899–1907.Google Scholar
  9. McCullagh, P. (1984). Local sufficiency,Biometrika,71, 233–244.Google Scholar
  10. McCullagh, P. (1987).Tensor Methods in Statistics, Chapman and Hall, London.Google Scholar
  11. Nicolaou, A. (1991). Bayesian intervals with good frequentist behavior in the presence of nuisance parameters,J. Roy. Statist. Soc. Ser. B,55(2), 377–390.Google Scholar
  12. Peers, H. W. (1965). On confidence points and Bayesian probability points in the case of several parameters,J. Roy. Statist. Soc. Ser. B,27, 9–16.Google Scholar
  13. Stein, C. (1982). On the coverage probability of confidence sets based on a prior distribution, Tech. Report, 180, Dept. of Statistics, Stanford University.Google Scholar
  14. Tibshirani, R. (1989). Noninformative priors for one parameter of many,Biometrika,76, 604–608.Google Scholar
  15. Welch, B. L. and Peers, H. W. (1963). On formulae for confidence points based on integrals of weighted likelihoods,J. Roy. Statist. Soc. Ser. B,25, 318–329.Google Scholar

Copyright information

© The Institute of Statistical Mathematics 1994

Authors and Affiliations

  • Anna Nicolaou
    • 1
  1. 1.Economic and Social SciencesUniversity of MacedoniaThessalonikiGreece

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