Monotonicity of Bayes estimators
Volume 40 / 2013
Applicationes Mathematicae 40 (2013), 393-404
MSC: 60E15, 62F15.
DOI: 10.4064/am40-4-1
Abstract
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.
