Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Inadmissibility of polynomial estimates of the shift parameter


In this note we demonstrate the inadmissibility of an extensive class of polynomial estimates of the shift parameter in the case of a quadratic loss function.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    A. M. Kagan, Yu. V. Linnik, and C. R. Rao, “On a characterization of the normal law based on a property of the sample average,” Sankhya, Ser. A,27, No. 3–4, 405–406 (1965).

  2. 2.

    A. M. Kagan, “Theory of estimation for families with shift, scaling, and exponentiation parameters,” Trudy Matem. Inst. Akad. Nauk SSSR.104 (1968).

  3. 3.

    A. M. Kagan, Yu. V. Linnik, and C. R. Rao, Characterizational Problems of Mathematical Statistics [in Russian], Moscow (1972).

  4. 4.

    A. A. Zinger, “Independence of quasipolynomial statistics and analytical properties of distributions,” Teor. Veroyatn. i ee Primen.,3, No. 3, 262–284 (1958).

  5. 5.

    V. V. Golubev, Lectures on the Analytic Theory of Differential Equations [in Russian], Moscow-Leningrad (1950).

  6. 6.

    Yu. V. Linnik, “On polynomial statistics in connection with the analytic theory of differential equations,” Vestnik Leningrad Gos. Univ.,1, 35–48 (1956).

  7. 7.

    J. Marcinkiewicz, “Sur une propriete de la loi de Gauss,” Math. Zeitschr.,44, No. 4–5, 622–638 (1938).

  8. 8.

    H. Wittich, Recent Research on Single-Valued Analytic Functions [Russian translation], Moscow (1960).

Download references

Author information

Additional information

Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 885–894, December, 1973.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Klebanov, L.B. Inadmissibility of polynomial estimates of the shift parameter. Mathematical Notes of the Academy of Sciences of the USSR 14, 1068–1073 (1973).

Download citation


  • Loss Function
  • Polynomial Estimate
  • Shift Parameter
  • Quadratic Loss
  • Extensive Class