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Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error

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Abstract

In this paper, we propose a Bayesian method to estimate the underlying density function of a study variable Y using a ranked set sample in which an auxiliary variable X is used to rank the sampling units. The amount of association between X and Y is not known, resulting in an unknown degree of ranking error. We assume that (X, Y) follows a Morgenstern family of distributions. The study variable Y is assumed to have a parametric distribution, with the distribution of the parameters having a Dirichlet process prior. A Markov chain Monte Carlo procedure is developed to obtain a Bayesian estimator of the desired density function as well as of the ranking error. A simulation study is used to evaluate the performance of the proposed method. An example from forestry is used to illustrate a real-life application of the proposed methodology.

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Acknowledgments

The authors are grateful to the referees for their valuable comments and suggestions. The first author is thankful to University Grants Commission, Govt. of India for providing financial support in the form of Raman Fellowship for Post Doctoral Research for Indian Scholars in USA. The first author is also thankful to the Department of Mathematical Sciences, University of Nevada Las Vegas for giving necessary facilities to do this work. The second author would like to thank University of Nevada Las Vegas for sabbatical leave during which part of this work was accomplished

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  1. Manoj Chacko

    Present address: Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV, 89154, USA

Authors and Affiliations

  1. Department of Statistics, University of Kerala, Trivandrum, 695581, India

    Manoj Chacko

  2. Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV, 89154, USA

    Kaushik Ghosh

Authors
  1. Manoj Chacko
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  2. Kaushik Ghosh
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Correspondence to Manoj Chacko.

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Handling Editor: Pierre Dutilleul.

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Chacko, M., Ghosh, K. Semi-parametric Bayesian density estimation using ranked set sample in the presence of ranking error. Environ Ecol Stat 23, 301–316 (2016). https://doi.org/10.1007/s10651-016-0340-4

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  • DOI: https://doi.org/10.1007/s10651-016-0340-4

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