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On the performance of estimation methods under ranked set sampling

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  • Cesar Augusto Taconeli

    (Federal University of Paraná)

  • Wagner Hugo Bonat

    (Federal University of Paraná)

Abstract

Maximum likelihood estimation (MLE) applied to ranked set sampling (RSS) designs is usually based on the assumption of perfect ranking. However, it may suffers of lack of efficiency when ranking errors are present. The main goal of this article is to investigate the performance of six alternative estimation methods to MLE for parameter estimation under RSS. We carry out an extensive simulation study and measure the performance of the maximum product of spacings, ordinary and weighted least-squares, Cramér-von-Mises, Anderson–Darling and right-tail Anderson–Darling estimators, along with the maximum likelihood estimators, through the Kullback–Leibler divergence from the true and estimated probability density functions. Our simulation study considered eight continuous probability distributions, six sample sizes and six levels of correlation between the interest and concomitant variables. In general, our results show that the Anderson–Darling method outperforms its competitors and that the maximum likelihood estimators strongly depends on perfect ranking for accurate estimation. Finally, we present an illustrative example using a data set concerning the percent of body fat. R code is available in the supplementary material.

Suggested Citation

  • Cesar Augusto Taconeli & Wagner Hugo Bonat, 2020. "On the performance of estimation methods under ranked set sampling," Computational Statistics, Springer, vol. 35(4), pages 1805-1826, December.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00953-9
    DOI: 10.1007/s00180-020-00953-9
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    References listed on IDEAS

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    1. Modarres, Reza & Hui, Terrence P. & Zheng, Gang, 2006. "Resampling methods for ranked set samples," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1039-1050, November.
    2. Giovani Carrara Rodrigues & Francisco Louzada & Pedro Luiz Ramos, 2018. "Poisson–exponential distribution: different methods of estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 128-144, January.
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    Cited by:

    1. Yusuf Can Sevil & Tugba Ozkal Yildiz, 2022. "Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling," Computational Statistics, Springer, vol. 37(4), pages 1695-1726, September.
    2. Cesar Augusto Taconeli & Idemauro Antonio Rodrigues Lara, 2022. "Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach," Computational Statistics, Springer, vol. 37(5), pages 2267-2293, November.
    3. Heba F. Nagy & Amer Ibrahim Al-Omari & Amal S. Hassan & Ghadah A. Alomani, 2022. "Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data," Mathematics, MDPI, vol. 10(21), pages 1-19, November.
    4. Manal M. Yousef & Amal S. Hassan & Abdullah H. Al-Nefaie & Ehab M. Almetwally & Hisham M. Almongy, 2022. "Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling," Mathematics, MDPI, vol. 10(17), pages 1-26, August.

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