Open Access
Translator Disclaimer
July, 1977 Admissibility of Linear Estimators in the One Parameter Exponential Family
Malay Ghosh, Glen Meeden
Ann. Statist. 5(4): 772-778 (July, 1977). DOI: 10.1214/aos/1176343899

Abstract

For estimating the mean in the one parameter exponential family with quadratic loss, Karlin (1958) gave sufficient conditions for admissibility of estimators of the form $aX$. Later, Ping (1964) and Gupta (1966) gave sufficient conditions for admissibility of estimators of the form $aX + b$ for the same problem. Zidek (1970) gave sufficient conditions for the admissibility of $X$ for estimating an arbitrary piecewise continuous function of the parameter, say $\gamma(\theta)$, not necessarily the mean. In this paper it is shown that Karlin's argument yields sufficient conditions for the admissibility of estimators of the form $aX + b$ for estimating $\gamma(\theta)$. The results are then extended to the case when the parameter space is truncated.

Citation

Download Citation

Malay Ghosh. Glen Meeden. "Admissibility of Linear Estimators in the One Parameter Exponential Family." Ann. Statist. 5 (4) 772 - 778, July, 1977. https://doi.org/10.1214/aos/1176343899

Information

Published: July, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0385.62006
MathSciNet: MR445662
Digital Object Identifier: 10.1214/aos/1176343899

Subjects:
Primary: 62C15
Secondary: 62F10

Keywords: Admissibility , Cramer-Rao inequality , generalized Bayes estimators , Linear estimators , one parameter exponential family , squared error loss , truncated parameter space

Rights: Copyright © 1977 Institute of Mathematical Statistics

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.5 • No. 4 • July, 1977
Back to Top