Monotonicity of Bayes estimators

Volume 40 / 2013

Jarosław Bartoszewicz, Piotr Bolesław Nowak Applicationes Mathematicae 40 (2013), 393-404 MSC: 60E15, 62F15. DOI: 10.4064/am40-4-1


Let $X=(X_1,\dots ,X_n)$ be a sample from a distribution with density $f(x;\theta )$, $\theta \in \Theta \subset \mathbb {R}$. In this article the Bayesian estimation of the parameter $\theta $ is considered. We examine whether the Bayes estimators of $\theta $ are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained.


  • Jarosław Bartoszewicz(deceased)
  • Piotr Bolesław NowakInstitute of Mathematics and Informatics
    University of Opole
    Oleska 48
    45-052 Opole, Poland

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