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The Families with a “Universal” Location Estimator

  • A. L. Rukhin
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 17)

Summary

The problem of estimating the multidimensional location parameter is considered. The new family of multivariate distribution is characterized by the property of the independence of the best equivariant estimator on the even loss function choice. Some generalizations of known functional equations are introduced and solved for this aim.

Key Words

Multidimensional location parameter loss function equivariant estimators completely symmetrical families D’Alembert’s functional equation 

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References

  1. [1]
    J. Aczel. (1966). Lectures on Functional Equations and Their Applications, Academic Press.zbMATHGoogle Scholar
  2. [2]
    A. M. Kagan, Yu. V. Linnik, C. R. Rao (1973). Characterization Problems in Mathematical Statistics. John Wiley and Sons, N. Y.zbMATHGoogle Scholar
  3. [3]
    L. Rejto (1972). Studia Sci. Math. Hung. 1, 331–336.MathSciNetGoogle Scholar
  4. [4]
    A. L. Rukhin (1970). Soviet Math. Dokl. II, 1, 89–92Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1975

Authors and Affiliations

  • A. L. Rukhin
    • 1
  1. 1.Mathematical InstituteLeningradUSSR

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