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Estimation of population proportion in randomized response sampling using weighted confidence interval construction

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Abstract

This paper considers the problem of estimation for binomial proportions of sensitive attributes in the population of interest. Randomized response techniques are suggested for protecting the privacy of respondents and reducing the response bias while eliciting information on sensitive attributes. By applying the Wilson (J Am Stat Assoc 22:209–212, 1927) score approach for constructing confidence intervals, various probable point estimators and confidence interval estimators are suggested for the common structures of randomized response procedures. In addition, efficiency comparisons are carried out to study the performances of the proposed estimators for both the cases of direct response surveys and randomized response surveys. Circumstances under which each proposed estimators is better are also identified.

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Authors and Affiliations

  1. Graduate Institute of Management Sciences, Tamkang University, Taipei, Taiwan

    Horng-Jinh Chang & Mei-Pei Kuo

  2. Department of Styling and Cosmetology, Tatung Institute of Commerce and Technology, Chiayi, Taiwan

    Mei-Pei Kuo

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  1. Horng-Jinh Chang
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  2. Mei-Pei Kuo
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Correspondence to Mei-Pei Kuo.

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Chang, HJ., Kuo, MP. Estimation of population proportion in randomized response sampling using weighted confidence interval construction. Metrika 75, 655–672 (2012). https://doi.org/10.1007/s00184-011-0346-8

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  • DOI: https://doi.org/10.1007/s00184-011-0346-8

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