Annals of Statistics

Admissibility of Linear Estimators in the One Parameter Exponential Family

Malay Ghosh and Glen Meeden

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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.

Article information

Source
Ann. Statist., Volume 5, Number 4 (1977), 772-778.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343899

Digital Object Identifier
doi:10.1214/aos/1176343899

Mathematical Reviews number (MathSciNet)
MR445662

Zentralblatt MATH identifier
0385.62006

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation

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

Citation

Ghosh, Malay; Meeden, Glen. Admissibility of Linear Estimators in the One Parameter Exponential Family. Ann. Statist. 5 (1977), no. 4, 772--778. doi:10.1214/aos/1176343899. https://projecteuclid.org/euclid.aos/1176343899


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