Skip to main content
SpringerLink
Log in

Admissibility of some preliminary test estimators for the mean of normal distribution

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

Let a random variableX follow ap-variate normal distributionNp(θ, Ip) with an unknownp×1 vector θ andp×p identity matrixIp. The admissibility of a preliminary test estimator using AIC (Akaike's Information Criterion) procedure will be shown ifp=1 and its inadmissibility will be shown ifp≧3 under the loss function based on Kullback-Leibler information measure. Furthermore the two sample case is also considered.

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. Blyth, C. R. (1951). On minimax statistical decision procedures and their admissibility,Ann. Math. Statist. 22, 22–42.

    Article  MathSciNet  Google Scholar 

  2. Hirano, K. (1977). Estimation procedures based on preliminary test, shrinkage technique and information criterion,Ann. Inst. Statist. Math.,29, 21–34.

    Article  MathSciNet  Google Scholar 

  3. Hirano, K. (1978). On level of significance of the preliminary test in pooling means,Ann. Inst. Statist. Math.,30, 1–8.

    Article  MathSciNet  Google Scholar 

  4. Inada, K. (1981). A minimax regret estimator of a normal mean after preliminary test,Proc. 50th Annual Meeting of Japan Statist. Soc., Kansai Univ. (in Japanese).

  5. Inagaki, N. (1977). Two errors in statistical model fitting,Ann. Inst. Statist. Math.,29, 131–152.

    Article  MathSciNet  Google Scholar 

  6. James, W. and Stein, C. (1961). Estimation with quadratic loss,Proc. 4th Berkeley Symp. Math. Statist. Prob.,1, 361–379.

    MathSciNet  MATH  Google Scholar 

  7. Meeden, G. and Arnold, B. C. (1979). The admissibility of a preliminary test estimator when the loss incorporates a complexity cost,J. Amer. Statist. Ass.,74, 872–874.

    Article  MathSciNet  Google Scholar 

  8. Sclove, S. L., Morris, C. and Radhakrishnan, R. (1972). Non-optimality of preliminary-test estimators for the mean of a multivariate normal distribution,Ann. Math. Statist.,43, 1481–1490.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Osaka University, Osaka, Japan

    Yasushi Nagata

Authors
  1. Yasushi Nagata
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Nagata, Y. Admissibility of some preliminary test estimators for the mean of normal distribution. Ann Inst Stat Math 35, 365–373 (1983). https://doi.org/10.1007/BF02480992

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02480992

Key words

Search

Navigation