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Metrika

, Volume 29, Issue 1, pp 115–128 | Cite as

Ungünstige Verteilungen bei einparametrigen Parameterschätzproblemen

  • E. Zinzius
Article
  • 18 Downloads

Summary

One of the commonly used methods for determining minimax point estimators is based on least favorable distributions, because Bayes estimators with respect to a least favorable distribution are frequently minimax point estimators. Therefore it is worthwhile to investigate the structure of least favorable distributions. In the present paper it will be proved that, under certain conditions, each least favorable distribution is finite discrete. We give sufficient conditions for point estimation problems with the property that each least favorable distribution is finite discrete. Some examples are presented.

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Literaturverzeichnis

  1. Dieudonné, J.: Grundzüge der modernen Analysis. Braunschweig 1971.Google Scholar
  2. Girshick, M.A., undL. Savage: Bayes and Minimax Estimates for Quadratic Loss Functions. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, 1851, 53–73.Google Scholar
  3. Hodges, J.L., undE.L. Lehmann: Some Problems in Minimax Point Estimation. AMS21, 1950, 182–197.Google Scholar
  4. Nelson, W.: Minimax Solution of Statistical Decision Problems by Iteration. AMS37, 1966, 1643–1657.Google Scholar
  5. Wald, A.: Statistical Decision Functions. New York 1950.Google Scholar
  6. Witting, H.: Mathematische Statistik. Stuttgart 1966.Google Scholar
  7. Zinzius, E.: Beiträge zur Theorie der nichtsequentiellen Parameterschätzprobleme. Dissertation, Karlsruhe 1979.Google Scholar

Copyright information

© Physica-Verlag 1982

Authors and Affiliations

  • E. Zinzius
    • 1
  1. 1.Mathematisches Institut IIUniversität KarlsruheKarlsruhe

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