Annals of the Institute of Statistical Mathematics

, Volume 45, Issue 3, pp 567–578 | Cite as

Inferential distributions for non-Bayesian predictive fit

  • Hisataka Kuboki
Estimation

Abstract

This article proposes a non-Bayesian procedure for constructing inferential distributions which can be used for producing predictive distributions. The concepts of bootstrap and of predictive likelihood are employed for developing the method. A result is obtained for exponential families, and the Bayesian prediction based on Jeffreys' prior is newly justified.

Key words and phrases

Bootstrap estimative fit exponential family inferential distribution Jeffreys' prior predictive distribution predictive fit predictive likelihood 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aitchison, J. (1975). Goodness of prediction fit,Biometrika,62, 547–554.Google Scholar
  2. Akaike, H. (1978). A new look at the Bayes procedure,Biometrika,65, 53–59.Google Scholar
  3. Barndorff-Nielsen, O. and Cox, D. R. (1979). Edgeworth and saddle-point approximations with statistical applications (with discussion),J. Roy. Statist. Soc. Ser. B,41, 279–312.Google Scholar
  4. Bernardo, J. M. (1979). Reference posterior distributions for Bayesian Inference (with discussion),J. Roy. Statist. Soc. Ser. B,41, 113–147.Google Scholar
  5. Bjørnstad, J. F. (1990). Predictive likelihood: a review,Statist. Sci.,5, 242–265.Google Scholar
  6. Box, G. E. P. and Tiao, G. C. (1973).Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading.Google Scholar
  7. Efron, B. (1982).The Jackknife, the Bootstrap and Other Resampling Plans, Regional Conference Series in Applied Mathematics, No. 38, SIAM, Philadelphia.Google Scholar
  8. El-Sayyad, G. M., Samiuddin, M. and Al-Harbey, A. A. (1989). On parametric density estimation,Biometrika,76, 343–348.Google Scholar
  9. Harris, I. R. (1989). Predictive fit for natural exponential families,Biometrika,76, 675–684.Google Scholar
  10. Hinkley, D. (1979). Predictive likelihood,Ann. Statist.,7, 718–728.Google Scholar
  11. Jeffreys, H. (1961).Theory of Probability, 3rd ed., Oxford University Press, Oxford.Google Scholar
  12. Kuboki, H. (1984). A generalization of the relative conditional expectation—further properties of Pitman'sT* and their applications to statistics,Ann. Inst. Statist. Math.,36, 181–197.Google Scholar
  13. Lauritzen, S. L. (1974). Sufficiency, prediction and extreme models,Scand. J. Statist.,2, 23–32.Google Scholar
  14. Mathiasen, P. E. (1979). Prediction Functions,Scand. J. Statist.,6, 1–21.Google Scholar
  15. Murray, G. D. (1977). A note on the estimation of probability density functions,Biometrika,64, 150–152.Google Scholar
  16. Ng, V. M. (1980). On the estimation of parametric density functions,Biometrika,67, 505–506.Google Scholar
  17. Olver, F. W. J. (1974).Asymptotics and Special Functions, Academic Press, New York.Google Scholar
  18. Pitman, E. J. G. (1979).Some Basic Theory for Statistical Inference, Chapman and Hall, London.Google Scholar

Copyright information

© The Institute of Statistical Mathematics 1993

Authors and Affiliations

  • Hisataka Kuboki
    • 1
  1. 1.Department of Communications and SystemsThe University of Electro-CommunicationsChofu, TokyoJapan

Personalised recommendations