## The Annals of Statistics

### Improving on Inadmissible Estimators in the Control Problem

L. Mark Berliner

#### Abstract

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 $p \geq 5$.

#### Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 814-826.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346248

Digital Object Identifier
doi:10.1214/aos/1176346248

Mathematical Reviews number (MathSciNet)
MR707932

Zentralblatt MATH identifier
0525.62009

JSTOR