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.
Publié le : 1977-07-14
Classification:
Admissibility,
one parameter exponential family,
linear estimators,
squared error loss,
generalized Bayes estimators,
Cramer-Rao inequality,
truncated parameter space,
62C15,
62F10
@article{1176343899,
author = {Ghosh, Malay and Meeden, Glen},
title = {Admissibility of Linear Estimators in the One Parameter Exponential Family},
journal = {Ann. Statist.},
volume = {5},
number = {1},
year = {1977},
pages = { 772-778},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343899}
}
Ghosh, Malay; Meeden, Glen. Admissibility of Linear Estimators in the One Parameter Exponential Family. Ann. Statist., Tome 5 (1977) no. 1, pp. 772-778. http://gdmltest.u-ga.fr/item/1176343899/