The Annals of Statistics

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

James O. Berger

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation 62H99: None of the above, but in this section

Keywords
Inadmissibility best invariant estimator location vector risk function loss function

Citation

Berger, James O. Inadmissibility Results for the Best Invariant Estimator of Two Coordinates of a Location Vector. Ann. Statist. 4 (1976), no. 6, 1065--1076. doi:10.1214/aos/1176343642. https://projecteuclid.org/euclid.aos/1176343642


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