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Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications

Author

Listed:
  • Seyf Alemam

    (Department of Statistics, University of Tabriz, P.O. Box 51666-17766, Tabriz 51666-16471, Iran)

  • Hazhir Homei

    (Department of Statistics, University of Tabriz, P.O. Box 51666-17766, Tabriz 51666-16471, Iran)

  • Saralees Nadarajah

    (Department of Mathematics, University of Manchester, Manchester M13 9PL, UK)

Abstract

Our aim in this paper is extending the applicability domain of the Rao–Blackwell theorem, our methodology is using conditional expectation and generalizing sufficient statistics, and one result is a generalization of the Lehmann–Scheffé theorem; as a conclusion, some problems that could not be solved by an earlier version of the Lehmann–Scheffé theorem become solvable by our new generalization.

Suggested Citation

  • Seyf Alemam & Hazhir Homei & Saralees Nadarajah, 2023. "Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications," Mathematics, MDPI, vol. 11(19), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4146-:d:1252107
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    References listed on IDEAS

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    1. L. Bondesson, 1983. "On uniformly minimum variance unbiased estimation when no complete sufficient statistics exist," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 30(1), pages 49-54, December.
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