The Annals of Statistics

Admissibility and Minaxity Results in the Estimation Problem of Exponential Quantiles

Andrew L. Rukhin

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Abstract

The estimation problem of the quantiles $\xi + b\sigma$ of an exponential distribution with unknown location-scale parameter $(\xi, \sigma)$ is considered. We establish the admissibility of the traditional (best equivariant) estimator for quadratic loss when $n^{-1} \leq b \leq 1 + n^{-1}$ where $n$ is the sample size. For $b > 1 + n^{-1}$ a class of minimax procedures is found. This class contains generalized Bayes rules and one of them is shown to be admissible within the class of scale-equivariant procedures.

Article information

Source
Ann. Statist., Volume 14, Number 1 (1986), 220-237.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349851

Digital Object Identifier
doi:10.1214/aos/1176349851

Mathematical Reviews number (MathSciNet)
MR829564

Zentralblatt MATH identifier
0599.62032

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62C15: Admissibility 62C20: Minimax procedures 62F11

Keywords
Exponential quantiles estimation quadratic loss minimaxity admissibility equivariance

Citation

Rukhin, Andrew L. Admissibility and Minaxity Results in the Estimation Problem of Exponential Quantiles. Ann. Statist. 14 (1986), no. 1, 220--237. doi:10.1214/aos/1176349851. https://projecteuclid.org/euclid.aos/1176349851


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