The Annals of Statistics

On Optimal Median Unbiased Estimators in the Presence of Nuisance Parameters

J. Pfanzagl

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 7, Number 1 (1979), 187-193.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344563

Digital Object Identifier
doi:10.1214/aos/1176344563

Mathematical Reviews number (MathSciNet)
MR515692

Zentralblatt MATH identifier
0399.62030

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation

Keywords
Estimators median unbiasedness nuisance parameters sufficiency completeness

Citation

Pfanzagl, J. On Optimal Median Unbiased Estimators in the Presence of Nuisance Parameters. Ann. Statist. 7 (1979), no. 1, 187--193. doi:10.1214/aos/1176344563. https://projecteuclid.org/euclid.aos/1176344563


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