Skip to main content
SpringerLink
Log in

Asymptotic normality under transformations. A result with Bayesian applications

  • Published:
Test Aims and scope Submit manuscript

Summary

A generalization is provided of the conditions to be satisfied in order to ensure asymptotic normality under transformations. From a Bayesian viewpoint, this result may be used to select an appropriate parameterization or to avoid additional calculations when the parameter of interest does not coincide with the usual parameter of the model.

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

  • Anderson, S. A., Brons, H. K., and Jensen, S. T. (1983). Distribution of eigenvalues in multivariate statistical analysis.Ann. Statist. 11, 392–415.

    MathSciNet  Google Scholar 

  • Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference.J. Roy. Statist. Soc. B 41, 113–147, (with discussion).

    MathSciNet  MATH  Google Scholar 

  • Box, G.E.P., and Tiao, G.C. (1973).Bayesian Inference in Statistical Analysis. Reading, MA: Addison-Wesley.

    MATH  Google Scholar 

  • Cramér, H. (1946).Mathematical Methods of Statistics. Princeton: University Press.

    MATH  Google Scholar 

  • Chen, Ch. (1985) On asymptotic normality of limiting density functions with Bayesian implications.J. Roy. Statist. Soc. B 47, 540–546.

    MATH  Google Scholar 

  • Dawid, A. P. (1970). On the limiting normality of posterior distributions.Proc. Camb. Phil. Soc. 67, 625–633.

    Article  MathSciNet  MATH  Google Scholar 

  • DeGroot, M. H. (1970).Optimal Statistical Decisions. New York: McGraw-Hill.

    MATH  Google Scholar 

  • Efron, B. (1986). Why isn’t everyone a Bayesian?Amer. Statist. 40, 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  • Fraser, D. A. S. and McDunnough, P. (1984). Further remarks on asymptotic normality of likelihood and conditional analyses.Canadian J. Statist. 12, 183–190.

    MathSciNet  MATH  Google Scholar 

  • Heyde, C. C. and Johnstone, I. M. (1979). On asymptotic posterior normality for stochastic processes.J. Roy. Statist. Soc. B 41, 184–189.

    MathSciNet  MATH  Google Scholar 

  • Johnson, R. A. (1967). An asymptotic expansion for posterior distributions.Ann. Math. Statist. 38, 1899–1907.

    MathSciNet  MATH  Google Scholar 

  • Johnson, R. A. (1970). Asymptotic expansions associated with posterior distributions.Ann. Math. Statist. 41, 851–854.

    MathSciNet  MATH  Google Scholar 

  • Lindley, D. V. (1965).Introduction to Probability and Statistics from a Bayesian viewpoint. Cambridge: University Press.

    MATH  Google Scholar 

  • Le Cam, L. (1958). Les propietés asymptotiques des solutions Bayes.Pub. de Inst. de Statist. de Univ. de Paris 7, 17–35.

    Google Scholar 

  • Press, S. J. (1982).Applied Multivariate Analysis using Bayesian and Frequentist Methods of Inference, Florida: Krieger.

    MATH  Google Scholar 

  • Slutsky, E. (1925). Uber Stochastische Asymptoten and Grenzwerte.Metron 5, 3, 3.

    Google Scholar 

  • Serfling, R. J. (1980).Approximation Theorems of Mathematical Statistics. New York: Wiley.

    MATH  Google Scholar 

  • Stein, C. (1982). The coverage probability of confidence sets based on a prior distribution.Tech. Rep. 180, Standford University.

  • Walker, A. M. (1969). On asymptotic behaviour of posterior distributions.J. Roy. Statist. Soc. B 31, 80–88.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estadística, Instituto Tecnológico Autónomo de México, Río Hondo 1, San Angel, 1000, México, D.F., MEXICO

    Manuel Mendoza

Authors
  1. Manuel Mendoza
    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

Mendoza, M. Asymptotic normality under transformations. A result with Bayesian applications. Test 3, 173–180 (1994). https://doi.org/10.1007/BF02562699

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02562699

Keywords

Search

Navigation