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February 2020 On estimating the location parameter of the selected exponential population under the LINEX loss function
Mohd Arshad, Omer Abdalghani
Braz. J. Probab. Stat. 34(1): 167-182 (February 2020). DOI: 10.1214/18-BJPS407

Abstract

Suppose that $\pi_{1},\pi_{2},\ldots ,\pi_{k}$ be $k(\geq2)$ independent exponential populations having unknown location parameters $\mu_{1},\mu_{2},\ldots,\mu_{k}$ and known scale parameters $\sigma_{1},\ldots,\sigma_{k}$. Let $\mu_{[k]}=\max \{\mu_{1},\ldots,\mu_{k}\}$. For selecting the population associated with $\mu_{[k]}$, a class of selection rules (proposed by Arshad and Misra [Statistical Papers 57 (2016) 605–621]) is considered. We consider the problem of estimating the location parameter $\mu_{S}$ of the selected population under the criterion of the LINEX loss function. We consider three natural estimators $\delta_{N,1},\delta_{N,2}$ and $\delta_{N,3}$ of $\mu_{S}$, based on the maximum likelihood estimators, uniformly minimum variance unbiased estimator (UMVUE) and minimum risk equivariant estimator (MREE) of $\mu_{i}$’s, respectively. The uniformly minimum risk unbiased estimator (UMRUE) and the generalized Bayes estimator of $\mu_{S}$ are derived. Under the LINEX loss function, a general result for improving a location-equivariant estimator of $\mu_{S}$ is derived. Using this result, estimator better than the natural estimator $\delta_{N,1}$ is obtained. We also shown that the estimator $\delta_{N,1}$ is dominated by the natural estimator $\delta_{N,3}$. Finally, we perform a simulation study to evaluate and compare risk functions among various competing estimators of $\mu_{S}$.

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Mohd Arshad. Omer Abdalghani. "On estimating the location parameter of the selected exponential population under the LINEX loss function." Braz. J. Probab. Stat. 34 (1) 167 - 182, February 2020. https://doi.org/10.1214/18-BJPS407

Information

Received: 1 September 2017; Accepted: 1 June 2018; Published: February 2020
First available in Project Euclid: 3 February 2020

zbMATH: 07200398
MathSciNet: MR4058977
Digital Object Identifier: 10.1214/18-BJPS407

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 1 • February 2020
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