Let $X$ have a $p$-variate normal distribution with unknown mean $\theta$ and identity covariance matrix. The following transformed version of a control problem (Zaman, 1981) is considered: estimate $\theta$ by $d$ subject to incurring a loss $L(d, \theta) = (\theta^t d - 1)^2$. The comparison of decision rules in terms of expected loss is reduced to the study of differential inequalities. Results establishing the minimaxity of a large class of estimators are obtained. Special attention is given to the proposition of admissible, generalized Bayes rules which dominate the uniform prior, generalized Bayes controller when $p \geq 5$.
Publié le : 1983-09-14
Classification:
Admissibility,
inadmissibility,
generalized Bayes rules,
control problem,
differential inequalities,
multivariate normal distribution,
62F10,
62C15,
62H99
@article{1176346248,
author = {Berliner, L. Mark},
title = {Improving on Inadmissible Estimators in the Control Problem},
journal = {Ann. Statist.},
volume = {11},
number = {1},
year = {1983},
pages = { 814-826},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346248}
}
Berliner, L. Mark. Improving on Inadmissible Estimators in the Control Problem. Ann. Statist., Tome 11 (1983) no. 1, pp. 814-826. http://gdmltest.u-ga.fr/item/1176346248/