## The Annals of Statistics

### Inadmissibility Results for the Best Invariant Estimator of Two Coordinates of a Location Vector

James O. Berger

#### Abstract

Let $X = (X_1, X_2, X_3)$ be a random vector with density $f(x - \theta)$, where $\theta = (\theta_1, \theta_2, \theta_3)$ is unknown. It is desired to estimate $(\theta_1, \theta_2)$ using an estimator $(\delta_1(X), \delta_2(X))$, and under a loss function $L(\delta_1 - \theta_1, \delta_2 - \theta_2)$. (Note that $\theta_3$ is a nuisance parameter.) Under certain conditions on $f$ and $L$, it is shown that the best invariant estimator of $(\theta_1, \theta_2)$ is inadmissible.

#### Article information

Source
Ann. Statist., Volume 4, Number 6 (1976), 1065-1076.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343642

Digital Object Identifier
doi:10.1214/aos/1176343642

Mathematical Reviews number (MathSciNet)
MR438542

Zentralblatt MATH identifier
0344.62006

JSTOR