On Optimal Median Unbiased Estimators in the Presence of Nuisance Parameters
The Annals of Statistics · 1979 · Volume 7 · Issue 1
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.
Keywords
62F10, completeness, Estimators, median unbiasedness, nuisance parameters, sufficiency
Enable JavaScript for citation tools and additional paper interactions.