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

Gajendra K. Vishwakarma (), Amod Kumar () and Neelesh Kumar ()
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Gajendra K. Vishwakarma: Indian Institute of Technology Dhanbad
Amod Kumar: Indian Institute of Technology Dhanbad
Neelesh Kumar: Indian Institute of Technology Dhanbad

Computational Statistics, 2024, vol. 39, issue 2, No 19, 865-890

Abstract: 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.

Keywords: Poisson probability distribution; Unrelated randomized response model; Sensitive attribute; Estimation of proportion; Privacy protection; 62D05; 62K15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01326-8

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