Brazilian Journal of Probability and Statistics

On estimating the scale parameter of the selected uniform population under the entropy loss function

Mohd. Arshad and Neeraj Misra

Full-text: Open access

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.

Article information

Source
Braz. J. Probab. Stat., Volume 31, Number 2 (2017), 303-319.

Dates
Received: July 2015
Accepted: February 2016
First available in Project Euclid: 14 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1492156964

Digital Object Identifier
doi:10.1214/16-BJPS314

Mathematical Reviews number (MathSciNet)
MR3635907

Zentralblatt MATH identifier
1370.62014

Keywords
Estimation after selection uniform population inadmissible estimators entropy loss function natural selection rule

Citation

Arshad, Mohd.; Misra, Neeraj. On estimating the scale parameter of the selected uniform population under the entropy loss function. Braz. J. Probab. Stat. 31 (2017), no. 2, 303--319. doi:10.1214/16-BJPS314. https://projecteuclid.org/euclid.bjps/1492156964


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