## Annals of Statistics

### Admissibility of Linear Estimators in the One Parameter Exponential Family

#### 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

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