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Bayesian Estimation Using Expected LINEX Loss Function: A Novel Approach with Applications

Author

Listed:
  • Mazen Nassar

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt)

  • Refah Alotaibi

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Hassan Okasha

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt)

  • Liang Wang

    (School of Mathematics, Yunnan Normal University, Kunming 650092, China)

Abstract

The loss function plays an important role in Bayesian analysis and decision theory. In this paper, a new Bayesian approach is introduced for parameter estimation under the asymmetric linear-exponential (LINEX) loss function. In order to provide a robust estimation and avoid making subjective choices, the proposed method assumes that the parameter of the LINEX loss function has a probability distribution. The Bayesian estimator is then obtained by taking the expectation of the common LINEX-based Bayesian estimator over the probability distribution. This alternative proposed method is applied to estimate the exponential parameter by considering three different distributions of the LINEX parameter, and the associated Bayes risks are also obtained in consequence. Extensive simulation studies are conducted in order to compare the performance of the proposed new estimators. In addition, three real data sets are analyzed to investigate the applicability of the proposed results. The results of the simulation and real data analysis show that the proposed estimation works satisfactorily and performs better than the conventional standard Bayesian approach in terms of minimum mean square error and Bayes risk.

Suggested Citation

  • Mazen Nassar & Refah Alotaibi & Hassan Okasha & Liang Wang, 2022. "Bayesian Estimation Using Expected LINEX Loss Function: A Novel Approach with Applications," Mathematics, MDPI, vol. 10(3), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:436-:d:737906
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    References listed on IDEAS

    as
    1. Yen-chang Chang & Wen-liang Hung, 2007. "LINEX Loss Functions with Applications to Determining the Optimum Process Parameters," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(2), pages 291-301, April.
    2. Dey Dipak K. & Lou Kuo-ren & Bose Sudip, 1998. "A Bayesian Approach To Loss Robustness," Statistics & Risk Modeling, De Gruyter, vol. 16(1), pages 65-88, January.
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