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Parametric Inference Using Nomination Sampling with an Application to Mercury Contamination in Fish

Author

Listed:
  • Mohammad Nourmohammadi

    (Statistical Research and Training Center of Iran)

  • Mohammad Jafari Jozani

    (University of Manitoba)

  • Brad C. Johnson

    (University of Manitoba)

Abstract

Randomized nomination sampling (RNS) is a rank-based sampling technique which has been shown to be effective in several nonparametric studies involving environmental, agricultural, medical and ecological applications. In this paper, we investigate parametric inference using RNS design for estimating an unknown vector of parameters θ in some parametric families of distributions. We examine both maximum likelihood (ML) and method of moments (MM) approaches. We introduce four types of RNS-based data as well as necessary EM algorithms for the ML estimation under each data type, and evaluate the performance of corresponding estimators in estimating θ compared with those based on simple random sampling (SRS). Our results can address many parametric inference problems in reliability theory, sport analytics, fisheries, etc. Theoretical results are augmented with numerical evaluations, where we also study inference based on imperfect ranking. We apply our methods to a real data problem in order to study the distribution of the mercury contamination in fish body using RNS designs.

Suggested Citation

  • Mohammad Nourmohammadi & Mohammad Jafari Jozani & Brad C. Johnson, 2020. "Parametric Inference Using Nomination Sampling with an Application to Mercury Contamination in Fish," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 115-146, February.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:1:d:10.1007_s13171-018-00159-8
    DOI: 10.1007/s13171-018-00159-8
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    References listed on IDEAS

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    1. Debasis Bhattacharya & Francisco J. Samaniego, 2010. "Estimating component characteristics from system failure‐time data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 380-389, June.
    2. Kaushik Ghosh & Ram Tiwari, 2009. "A unified approach to variations of ranked set sampling with applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 471-485.
    3. Nader Gemayel & Elizabeth Stasny & Douglas Wolfe, 2010. "Optimal ranked set sampling estimation based on medians from multiple set sizes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 517-527.
    4. Nourmohammadi, Mohammad & Jafari Jozani, Mohammad & Johnson, Brad C., 2014. "Confidence intervals for quantiles in finite populations with randomized nomination sampling," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 112-128.
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