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May 2017 On estimating the scale parameter of the selected uniform population under the entropy loss function
Mohd. Arshad, Neeraj Misra
Braz. J. Probab. Stat. 31(2): 303-319 (May 2017). DOI: 10.1214/16-BJPS314

Abstract

Let $\pi_{1},\ldots,\pi_{k}$ be $k$ ($\geq2$) independent populations, where $\pi_{i}$ denotes the uniform distribution over the interval $(0,\theta_{i})$ and $\theta_{i}>0$ ($i=1,\ldots,k$) is an unknown scale parameter. Let $\theta_{[1]}\leq\cdots\leq\theta_{[k]}$ be the ordered values of $\theta_{1},\ldots,\theta_{k}$. The population $\pi_{(k)}$ ($\pi_{(1)}$) associated with the unknown parameter $\theta_{[k]}$ ($\theta_{[1]}$) is called the best (worst) population. For selecting the best population, we consider a general class of selection rules based on the natural estimators of $\theta_{i},i=1,\ldots,k$. Under the entropy loss function, we consider the problem of estimating the scale parameter $\theta_{S}$ of the population selected using a fixed selection rule from this class. We derive the uniformly minimum risk unbiased estimator of $\theta_{S}$ and two natural estimators of $\theta_{S}$ are also considered. We derive a general result for improving a scale invariant estimator of $\theta_{S}$ under the entropy loss function. A simulation study on the performances of various competing estimators of $\theta_{S}$ is also reported. Finally, we provide similar results for the problem of estimating the scale parameter of selected population when the selection goal is that of selecting the worst uniform population.

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Mohd. Arshad. Neeraj Misra. "On estimating the scale parameter of the selected uniform population under the entropy loss function." Braz. J. Probab. Stat. 31 (2) 303 - 319, May 2017. https://doi.org/10.1214/16-BJPS314

Information

Received: 1 July 2015; Accepted: 1 February 2016; Published: May 2017
First available in Project Euclid: 14 April 2017

zbMATH: 1370.62014
MathSciNet: MR3635907
Digital Object Identifier: 10.1214/16-BJPS314

Rights: Copyright © 2017 Brazilian Statistical Association

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Vol.31 • No. 2 • May 2017
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