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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barndorff-Nielsen, O. E. (1986). Inference on full or partial parameters based on the standardized signed log likelihood ratio,Biometrika,73, 307–322.
Barndorff-Nielsen, O. E. (1991). Modified signed log likelihood ratio,Biometrika,78, 557–563.
Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion),J. Roy. Statist. Soc. Ser. B,41, 113–147.
Cox, D. R. (1980). Local ancillarity,Biometrika,67, 279–286.
Cox, D. R. and Reid, R. (1987). Orthogonal parameters and approximate conditional inference (with discussion),J. Roy. Statist. Soc. Ser. B,49, 1–39.
DeBruijn, N. C. (1981).Asymptotic Methods in Analysis, Dover, New York.
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.
Johnson, R. A. (1970). An asymptotic expansion for posterior distributions,Ann. Math. Statist.,38, 1899–1907.
McCullagh, P. (1984). Local sufficiency,Biometrika,71, 233–244.
McCullagh, P. (1987).Tensor Methods in Statistics, Chapman and Hall, London.
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.
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.
Stein, C. (1982). On the coverage probability of confidence sets based on a prior distribution, Tech. Report, 180, Dept. of Statistics, Stanford University.
Tibshirani, R. (1989). Noninformative priors for one parameter of many,Biometrika,76, 604–608.
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.
Author information
Authors and Affiliations
About this article
Cite this article
Nicolaou, A. Conditional properties of Bayesian interval estimates. Ann Inst Stat Math 46, 21–28 (1994). https://doi.org/10.1007/BF00773589
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00773589