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Two-stage unrelated randomized response model to estimate the prevalence of a sensitive attribute

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Abstract

The present work proposes a new two-stage unrelated randomized response model to estimate the mean number of individuals who possess a rare sensitive attribute in a given population by using Poisson probability distribution, when the proportion of rare non-sensitive unrelated attribute is known and unknown. The properties of the proposed model are examined. The variance of the proposed randomized response model smaller than Land et al. (Stat J Theor Appl Stat, 46(3):351–360, 2012) and Singh and Tarray (Model Assist Stat Appl, 10(2):129–138, 2015) to estimate sensitive characteristic under study. The proposed model provides a more efficient unbiased estimator of the mean number of individuals. The procedure also introduces the measure of privacy protection of respondents and compares randomized response models in terms of efficiency and privacy protection. Empirical illustrations are presented to support the theoretical results and suitable recommendations are put forward to the survey statisticians/practitioners.

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Acknowledgements

Authors are thankful to Editor Prof. Cathy W. S. Chen, the editorial board, and learned referees for their valuable comments which have made a substantial improvement to bring the original manuscript to its present form.

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No funding was received to carry out this research work.

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Authors and Affiliations

  1. Department of Mathematics & Computing, Indian Institute of Technology Dhanbad, Dhanbad, 826004, India

    Gajendra K. Vishwakarma, Amod Kumar & Neelesh Kumar

  2. Institute of Actuarial Science and Data Analytics, UCSI University, 56000, Kuala Lumpur, Malaysia

    Gajendra K. Vishwakarma

  3. Department of Mathematics, Swami Vivekanand Subharti University, Meerut, 250005, India

    Amod Kumar

  4. School of Studies in Statistics, Vikram University, Ujjain, 456010, India

    Neelesh Kumar

Authors
  1. Gajendra K. Vishwakarma
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  2. Amod Kumar
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  3. Neelesh Kumar
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All authors contributed equally and approved the final manuscript.

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Correspondence to Amod Kumar.

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Vishwakarma, G.K., Kumar, A. & Kumar, N. Two-stage unrelated randomized response model to estimate the prevalence of a sensitive attribute. Comput Stat 39, 865–890 (2024). https://doi.org/10.1007/s00180-023-01326-8

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  • DOI: https://doi.org/10.1007/s00180-023-01326-8

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