The Annals of Statistics
- Ann. Statist.
- Volume 11, Number 3 (1983), 814-826.
Improving on Inadmissible Estimators in the Control Problem
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 $p \geq 5$.
Ann. Statist., Volume 11, Number 3 (1983), 814-826.
First available in Project Euclid: 12 April 2007
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Berliner, L. Mark. Improving on Inadmissible Estimators in the Control Problem. Ann. Statist. 11 (1983), no. 3, 814--826. doi:10.1214/aos/1176346248. https://projecteuclid.org/euclid.aos/1176346248