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August 2020 Improved estimators of the entropy in scale mixture of exponential distributions
Constantinos Petropoulos, Lakshmi Kanta Patra, Somesh Kumar
Braz. J. Probab. Stat. 34(3): 580-593 (August 2020). DOI: 10.1214/19-BJPS450

Abstract

In the present communication, the problem of estimating entropy of a scale mixture of exponential distributions is considered under the squared error loss. Inadmissibility of the best affine equivariant estimator(BAEE) is established by deriving an improved estimator which is not smooth. Using the integral expression of risk difference (IERD) approach of Kubokawa (The Annals of Statistics 22 (1994) 290–299), classes of estimators are obtained which improve upon the BAEE. The boundary estimator of this class is the Brewster and Zidek-type estimator and this estimator is smooth. We have shown that the Brewster and Zidek-type estimator is a generalized Bayes estimator. As an application of these results, we have obtained improved estimators for the entropy of a multivariate Lomax distribution. Finally, percentage risk reduction of the improved estimators for the entropy of a multivariate Lomax distribution is plotted to compare the risk performance of the improved estimators.

Citation

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Constantinos Petropoulos. Lakshmi Kanta Patra. Somesh Kumar. "Improved estimators of the entropy in scale mixture of exponential distributions." Braz. J. Probab. Stat. 34 (3) 580 - 593, August 2020. https://doi.org/10.1214/19-BJPS450

Information

Received: 1 February 2018; Accepted: 1 May 2019; Published: August 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07232913
MathSciNet: MR4124541
Digital Object Identifier: 10.1214/19-BJPS450

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 3 • August 2020
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