The Annals of Statistics

Improving on Inadmissible Estimators in the Control Problem

L. Mark Berliner

Full-text: Open access

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


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