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Estimating Sensitive Population Proportion Using a Combination of Binomial and Hypergeometric Randomized Responses by Direct and Inverse Mechanism

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  • Dihidar Kajal

    (Sampling and Official Statistics Unit, Indian Statistical Institute, Kolkata, India)

  • Bhattacharya Manjima

    (Credit Swiss Company, Mumbai, Maharastra, India)

Abstract

For various reasons individuals in a sample survey may prefer not to confide to the interviewer the correct answers to certain potentially sensitive questions such as the illegal use of drugs, illegal earning, or incidence of acts of domestic violence, etc. In such cases the individuals may elect not to reply at all or to reply with incorrect answers. The resulting evasive answer bias is ordinarily difficult to assess. The use of a randomized response method for estimating the proportion of individuals possessing those sensitive attributes can potentially eliminate the bias. Following Chaudhuri and Dihidar (2014) and Dihidar (2016), here, as a possible variant, we have made an attempt to estimate the sensitive population proportion using a combination of binomial and hypergeometric randomized responses by direct and inverse mechanism. Along with the traditional simple random sampling, with and without replacement, we consider here sampling of respondents by unequal probabilities. Essential theoretical derivations for unbiased estimator, variance and variance estimators are presented for several sampling schemes. A numerical illustration is performed to make a comparative study of the relative efficiencies of the direct and inverse mechanism.

Suggested Citation

  • Dihidar Kajal & Bhattacharya Manjima, 2017. "Estimating Sensitive Population Proportion Using a Combination of Binomial and Hypergeometric Randomized Responses by Direct and Inverse Mechanism," Statistics in Transition New Series, Statistics Poland, vol. 18(2), pages 193-210, June.
    • Handle: RePEc:vrs:stintr:v:18:y:2017:i:2:p:193-210:n:9
    DOI: 10.21307/stattrans-2016-066
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    References listed on IDEAS

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    1. Arijit Chaudhuri & Mausumi Bose & Kajal Dihidar, 2011. "Estimation of a sensitive proportion by Warner’s randomized response data through inverse sampling," Statistical Papers, Springer, vol. 52(2), pages 343-354, May.
    2. Arijit Chaudhuri & Mausumi Bose & Kajal Dihidar, 2011. "Estimating sensitive proportions by Warner’s randomized response technique using multiple randomized responses from distinct persons sampled," Statistical Papers, Springer, vol. 52(1), pages 111-124, February.
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    4. Sarjinder Singh & Stephen Sedory, 2013. "A new randomized response device for sensitive characteristics: an application of the negative hypergeometic distribution," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 3-8, June.
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    6. Shonkwiler, J.S., 2016. "Variance of the truncated negative binomial distribution," Journal of Econometrics, Elsevier, vol. 195(2), pages 209-210.
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