Skip to main content
SpringerLink
Log in

The lower bound for the variance of unbiased estimators for one-directional family of distributions

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

Summary

In this paper we introduce the concept of one-directionality which includes both cases of location (and scale) parameter and selection parameter and also other cases, and establish some theorems for shapr lower bounds and for the existence of zero variance unbiased estimator for this class of non-regular distributions.

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. Akahira, M., Puri, M. L. and Takeuchi, K. (1984). Bhattacharyya bound of variances of unbiased estimators in non-regular cases,Ann. Inst. Statist. Math.,38, 35–44.

    Article  Google Scholar 

  2. Chapman, D. G. and Robbins, H. (1951). Minimum variance estimation without regularity assumptions,Ann. Math. Statist.,22, 581–586.

    Article  MathSciNet  Google Scholar 

  3. Fraser, D. A. S. and Guttman, I. (1952). Bhattacharyya bounds without regularity assumptions,Ann. Math. Statist.,23, 629–632.

    Article  MathSciNet  Google Scholar 

  4. Kiefer, J. (1952). On minimum variance in non-regular estimation,Ann. Math. Statist.,23, 627–629.

    Article  Google Scholar 

  5. Móri, T. F. (1983). Note on the Cramér-Rao inequality in the non-regular cases: The family of uniform distributions,J. Statist. Plann. Inference,7, 353–358.

    Article  MathSciNet  Google Scholar 

  6. Morimoto, H. and Sibuya, M. (1967). Sufficient statistics and unbiased estimation of restricted selection parameter,Sankhyã, A27, 15–40.

    MathSciNet  MATH  Google Scholar 

  7. Takeuchi, K. and Akahira, M. (1983). A note on minimum variance,Metrika,33, 85–91.

    Article  MathSciNet  Google Scholar 

  8. Víncze, I. (1979). On the Cramér-Fréchet-Rao inequality in the non-regular case, InContributions to Statistics, the Jaroslav Hájek Memorial Volume, Academia, Prague, 253–262.

    Chapter  Google Scholar 

Download references

Author information

Author notes

  1. Masafumi Akahira & Kei Takeuchi

    Present address: University of Tsukuba, Tsukuba, Japan

Authors and Affiliations

  1. University of Electro-Communications, Tokyo

    Masafumi Akahira & Kei Takeuchi

  2. University of Tokyo, Tokyo, Japan

    Masafumi Akahira & Kei Takeuchi

Authors
  1. Masafumi Akahira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kei Takeuchi
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Akahira, M., Takeuchi, K. The lower bound for the variance of unbiased estimators for one-directional family of distributions. Ann Inst Stat Math 39, 593–610 (1987). https://doi.org/10.1007/BF02491492

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02491492

Key words and phrases

Search

Navigation