Let $X$ be a normal random variable with mean $\theta$ and variance 1 and consider the problem of estimating $\theta$ with squared error loss. If $\delta(x) = ax + b$ is a linear estimate with $0 \leqq a \leqq 1$ then it is well known that $\lambda\delta$ is an admissible proper Bayes estimate for $\lambda \in (0, 1)$. That is, all contractions of $\delta$ are proper Bayes estimates. In this note we show that no other estimates have this property.
Publié le : 1976-05-14
Classification:
Linear estimates,
normal distribution,
quadratic loss,
Bayes estimation,
62F10,
62C10
@article{1176343473,
author = {Meeden, Glen},
title = {A Special Property of Linear Estimates of the Normal Mean},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 649-650},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343473}
}
Meeden, Glen. A Special Property of Linear Estimates of the Normal Mean. Ann. Statist., Tome 4 (1976) no. 1, pp. 649-650. http://gdmltest.u-ga.fr/item/1176343473/