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March, 1986 Admissibility and Minaxity Results in the Estimation Problem of Exponential Quantiles
Andrew L. Rukhin
Ann. Statist. 14(1): 220-237 (March, 1986). DOI: 10.1214/aos/1176349851

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.

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Andrew L. Rukhin. "Admissibility and Minaxity Results in the Estimation Problem of Exponential Quantiles." Ann. Statist. 14 (1) 220 - 237, March, 1986. https://doi.org/10.1214/aos/1176349851

Information

Published: March, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0599.62032
MathSciNet: MR829564
Digital Object Identifier: 10.1214/aos/1176349851

Subjects:
Primary: 62F10
Secondary: 62C15, 62C20, 62F11

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 1 • March, 1986
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