Skip to main content
SpringerLink
Log in

An ɛ -admissibility condition on the sample mean as an estimator of a location parameter in the presence of a nuisance scale parameter

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

An estimate of stability is obtained in a theorem on characterizing the normal law by the property of sufficiency of the sample mean as an estimate of the location parameter in the presence of a nuisance scale parameter when the loss function is quadratic.

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

Literature cited

  1. A. M. Kagan, “On ε-admissibility of the sample mean as an estimator of location parameter,” Sankhya, Ser. A,32, 37–40 (1970).

    Google Scholar 

  2. A. M. Kagan, Yu. V. Linnik, and C. R. Rao, Characterization Problems in Mathematical Statistics, Wiley, New York (1973).

    Google Scholar 

  3. A. A. Zinger and A. M. Kagan, “Some statistical problems for families with location and scale parameters,” in: Proc. Int. Conf. Prob. Theory Math. Statist., Vilnius (1973).

  4. A. M. Kagan and A. A. Zinger, “Sample mean as an estimator of the location parameter in presence of the nuisance scale parameter,” Sankhya, Ser. A,35, 4 (1973).

    Google Scholar 

  5. L. Bondesson, “Characterizations of the normal and gamma distributions,” Z. Wahr. Verw. Geb.,26, 335–344 (1973).

    Google Scholar 

  6. L. B. Klebanov and I. A. Melamed, “On characterizing the normal and gamma distributions by properties of Fisher information,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,43 (1974).

  7. N. A. Sapogov, “Stability of solutions of functional equations related to problems of characterizing probability distributions,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,55 (1976).

  8. B. Ya. Levin, Distribution of Zeros of Entire Functions, Amer. Math. Society (1964).

  9. C. G. Esseen, “Fourier analysis of distribution functions,” Acta Math.,77, 1–125 (1945).

    Google Scholar 

Download references

Authors
  1. A. A. Zinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im V. A. Steklova AN SSSR, Vol. 61, pp. 25–37, 1976.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zinger, A.A. An ɛ -admissibility condition on the sample mean as an estimator of a location parameter in the presence of a nuisance scale parameter. J Math Sci 16, 1355–1364 (1981). https://doi.org/10.1007/BF01091627

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01091627

Keywords

Search

Navigation