We are concerned with the admissibility of nonlinear estimators of the form $(aX + b)/(cX + d)$ in the one-parameter exponential family, in estimating $g(\theta)$ with quadratic loss. Our method will be reminiscent of that of Karlin who gave sufficient conditions for admissibility of linear estimators $aX$ in estimating the mean in the one-parameter family. Our results generalize those of Ghosh and Meeden who studied admissibility of $aX + b$ for estimating an arbitrary function $g(\theta)$. Particular cases of estimators of the form, $c/X$ are studied and several examples are given. We show that $(n - 2)/(X + a), a \geq 0$ is admissible in estimating the parameter of an exponential density. We also discuss the case of truncated parameter space.
@article{1176345344,
author = {Ralescu, Dan and Ralescu, Stefan},
title = {A Class of Nonlinear Admissible Estimators in the One-Parameter Exponential Family},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 177-183},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345344}
}
Ralescu, Dan; Ralescu, Stefan. A Class of Nonlinear Admissible Estimators in the One-Parameter Exponential Family. Ann. Statist., Tome 9 (1981) no. 1, pp. 177-183. http://gdmltest.u-ga.fr/item/1176345344/