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

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.

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Acknowledgements

The authors gratefully acknowledge the partial support of the Natural Sciences and Engineering Research Council of Canada (NSERC). We would like to thank two anonymous referees for their useful comments.

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Correspondence to Mohammad Jafari Jozani.

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Nourmohammadi, M., Jafari Jozani, M. & Johnson, B.C. Parametric Inference Using Nomination Sampling with an Application to Mercury Contamination in Fish. Sankhya A 82, 115–146 (2020). https://doi.org/10.1007/s13171-018-00159-8

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Keywords

  • Randomized nomination sampling
  • Method of moments
  • Maximum likelihood
  • Modified maximum likelihood
  • EM algorithm

AMS (2000) subject classification.

  • Primary 62G05
  • Secondary 62D05