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Maximum Likelihood Estimation of Parameters of a Random Variable Using Monte Carlo Methods

Author

Listed:
  • Oualid Saci

    (University of Bejaia)

  • Megdouda Ourbih-Tari

    (Centre Universitaire de Tipaza
    Faculty of Exact Sciences University of Bejaia)

  • Leila Baiche

    (University of Bejaia)

Abstract

In a parametric estimation framework, this paper proposes different properties for the maximum likelihood estimators of unknown parameters of a given random variable having a known distribution, where different parameter estimation cases are studied. The Refined Descriptive Sampling (RDS) method is chosen to generate samples used for the estimation purpose. Then, we compare the RDS maximum likelihood estimators to their competitors provided by simple random samples with the same size and issued from the same distribution, through their Fisher information. Furthermore, the Maximum likelihood RDS mean is written as a function of its corresponding empirical estimator where the expression can be used to determine the estimator value when a refined descriptive sample is provided. All these results allow us to conclude that the proposed Maximum Likelihood Estimation (MLE) using refined descriptive samples is more efficient than that already obtained from simple random samples, which means that MLE using RDS has advantage in estimating parameters when the samples are not independent and identically distributed. Some Monte Carlo simulations are provided to validate the obtained theoretical results.

Suggested Citation

  • Oualid Saci & Megdouda Ourbih-Tari & Leila Baiche, 2023. "Maximum Likelihood Estimation of Parameters of a Random Variable Using Monte Carlo Methods," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 540-571, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00265-0
    DOI: 10.1007/s13171-021-00265-0
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    References listed on IDEAS

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    1. Leila Baiche & Megdouda Ourbih-Tari, 2017. "Large-sample variance of simulation using refined descriptive sampling: Case of independent variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 510-519, January.
    2. Abdelouhab Aloui & Arezki Zioui & Megdouda Ourbih-Tari & Amine Alioui, 2015. "A general purpose module using refined descriptive sampling for installation in simulation systems," Computational Statistics, Springer, vol. 30(2), pages 477-490, June.
    3. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
    4. Megdouda Ourbih-Tari & Mahdia Azzal, 2017. "Survival function estimation with non parametric adaptive refined descriptive sampling algorithm: A case study," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(12), pages 5840-5850, June.
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