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Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior

Author

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  • Meczarski, Marek
  • Zielinski, Ryszard

Abstract

The Bayesian estimator of the mean of the Poisson distribution under the gamma prior ([alpha]0, [beta]0) is stable (robust) in the sense that if the prior runs over the set {([alpha], [beta]0): [alpha][epsilon][[alpha]0-[delta], [alpha]0+[delta]]}, then the oscillat estimator with the oscillation O([delta]2) is constructed; it also minimizes the oscillation of the posterior risk when the shape parameter runs over a finite interval.

Suggested Citation

  • Meczarski, Marek & Zielinski, Ryszard, 1991. "Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 329-333, October.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:4:p:329-333
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    Citations

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    Cited by:

    1. Kiapour, A. & Nematollahi, N., 2011. "Robust Bayesian prediction and estimation under a squared log error loss function," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1717-1724, November.
    2. Ali Karimnezhad & Ahmad Parsian, 2018. "Most stable sample size determination in clinical trials," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 437-454, August.
    3. Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2012. "Bayesian and Robust Bayesian analysis under a general class of balanced loss functions," Statistical Papers, Springer, vol. 53(1), pages 51-60, February.
    4. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    5. Jafar Ahmadi & Elham Mirfarah & Ahmad Parsian, 2016. "Robust Bayesian Pitman closeness," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 671-691, August.

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