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Robust Bayesian Pitman closeness

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Abstract

In this paper, the robust Bayesian methodology has been developed in the sense of Pitman measure of closeness. To do this, the definition of Pitman posterior closeness, introduced by Ghosh and Sen (Commun Stat Theory Methods 20:3659–3678, 1991) and simultaneous closeness are integrated. First, the \(\varGamma \)-minimax problem is developed in the sense of Pitman’s criterion and the basic results and definitions are provided. Then, several results regarding Pitman \(\varGamma \)-minimax have been proved. Some examples have been presented to illustrate the application of the findings. Finally, other aspect of robust Bayesian methodology such as: Pitman stable rules and Pitman regret type estimators have been proposed.

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Acknowledgments

The authors are grateful to the two anonymous referees for making many helpful comments and suggestions on an earlier version of this paper. Ahmad Parsian’s research supported partially by a grant of the Research Council of the University of Tehran.

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Author notes

  1. Elham Mirfarah

    Present address: Department of Mathematics, Kharazmi University, Tehran, Iran

Authors and Affiliations

  1. Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, P. O. Box 91775-1159, Mashhad, Iran

    Jafar Ahmadi

  2. Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    Elham Mirfarah

  3. School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran

    Ahmad Parsian

Authors
  1. Jafar Ahmadi
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  2. Elham Mirfarah
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  3. Ahmad Parsian
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Correspondence to Jafar Ahmadi.

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Ahmadi, J., Mirfarah, E. & Parsian, A. Robust Bayesian Pitman closeness. Metrika 79, 671–691 (2016). https://doi.org/10.1007/s00184-015-0572-6

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