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Nonparametric maximum-likelihood estimation of within-set ranking errors in ranked set sampling

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  • Omer Ozturk

Abstract

A distribution-free statistical inference for the quality of within-set judgement ranking information is developed for ranked set samples. The judgement ranking information is modelled through Bohn–Wolfe (BW) model. The cumulative distribution function and the parameters of BW model are estimated by maximising nonparametric likelihood functions. A missing data model is introduced to construct an efficient computational algorithm. The advantages of the new estimators are that they require essentially no assumption on the underlying distribution function, which provides an estimate of the quality of within-set ranking information, and that they lead to a valid statistical inference even under imperfect ranking. The proposed estimators are applied to a water flow data set to estimate judgement ranking information and underlying distribution function.

Suggested Citation

  • Omer Ozturk, 2010. "Nonparametric maximum-likelihood estimation of within-set ranking errors in ranked set sampling," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 823-840.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:823-840
    DOI: 10.1080/10485250903287914
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    Cited by:

    1. Nikolay I. Nikolov & Eugenia Stoimenova, 2020. "Mallows’ models for imperfect ranking in ranked set sampling," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 459-484, September.
    2. Amer Ibrahim Al-Omari & Abdul Haq, 2012. "Improved quality control charts for monitoring the process mean, using double-ranked set sampling methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 745-763, August.
    3. Mohamed S. Abdallah & Amer I. Al-Omari & Naif Alotaibi & Ghadah A. Alomani & A. S. Al-Moisheer, 2022. "Estimation of distribution function using L ranked set sampling and robust extreme ranked set sampling with application to reliability," Computational Statistics, Springer, vol. 37(5), pages 2333-2362, November.
    4. Abdul Haq & Amer Al-Omari, 2015. "A new Shewhart control chart for monitoring process mean based on partially ordered judgment subset sampling," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 1185-1202, May.

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