Abstract
For exponential families with density \begin{equation*}x \rightarrow C(\theta, \eta)h(x)\exp\lbrack a(\theta)T(x) + \Sigma^p_{i=1} a_i(\theta, \eta)S_i(x)\rbrack, (\theta, \eta) \in \Theta \times H, \Theta \subset \mathbb{R},\end{equation*} $a$ increasing and continuous, there exists for every sample size an estimator for $\theta$ which is--in the class of all median unbiased estimators--of minimal risk for any monotone loss function.
Citation
J. Pfanzagl. "On Optimal Median Unbiased Estimators in the Presence of Nuisance Parameters." Ann. Statist. 7 (1) 187 - 193, January, 1979. https://doi.org/10.1214/aos/1176344563
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