## The Annals of Statistics

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

### Improving on Inadmissible Estimators in the Control Problem

#### 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**

links.jstor.org

**Subjects**

Primary: 62F10: Point estimation

Secondary: 62C15: Admissibility 62H99: None of the above, but in this section

**Keywords**

Admissibility inadmissibility generalized Bayes rules control problem differential inequalities multivariate normal distribution

#### Citation

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