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.
This paper considers the problem of procuring honest responses for sensitive quantitative characteristics. An alternative survey technique is proposed, which enables us to estimate the population mean unbiasedly and to gauge how sensitive a survey topic is. An asymptotically unbiased estimator of sensitivity level is proposed, and conditions for which unbiased estimation for population variance being available is also studied. In addition, an efficiency comparison is worked out to examine the performance of the proposed procedure. It is found that higher estimation efficiency results from higher variation of randomization device.
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