On the comparison of Warner's and unrelated question randomized response plans for estimating sensitive finite population proportions

S. Sengupta

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 5, 2370-2374

Abstract: We consider the problem of estimation of a finite population proportion (P) related to a sensitive attribute under Warner's (1965) randomized response plan and the unrelated question plan due to Horvitz et al. (1967) and prove that for a given probability sampling design, given any linear unbiased estimator (LUE) of P based on Warner's (1965) plan with any given value of the plan parameter, there exists an LUE of P based on the unrelated question plan with a uniformly smaller variance for suitable choices of the plan parameters. Assuming that only the attribute is sensitive but its complement is innocuous, the same is also shown to be true when the plan parameters for the two plans are so chosen so that both offer the same specified level of privacy.

Date: 2017
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DOI: 10.1080/03610926.2015.1044669

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