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A mixture of true and randomized responses in the estimation of the number of people having a certain attribute. (English) Zbl 1365.62045
Chaudhuri, Arijit (ed.) et al., Data gathering, analysis and protection of privacy through randomized response techniques: qualitative and quantitative human traits. Amsterdam: Elsevier/North Holland (ISBN 978-0-444-63570-9/hbk; 978-0-444-63571-6/ebook). Handbook of Statistics 34, 105-117 (2016).
Summary: In practice, when sensitive information is asked from survey units by an indirect questioning technique, some of the respondents may be willing to divulge their true values of the sensitive variable even without being asked. For instance, while explaining a randomized response (RR) method, the interviewee may say “Stop the explanations – I don’t mind answering this question directly!” With respect to estimation accuracy, such an offer must not be ignored. For the estimation of a group size, an RR questioning design allowing such a mixture of true and masked answers is discussed for general probability sampling applying a Horvitz-Thompson type estimator. This estimation process, including compensation for nonresponse, can be vividly illustrated by the concept of pseudo-populations. In the author’s teaching experience, this can improve the comprehension of the estimation process especially for those with only little knowledge of probability theory.
For the entire collection see [Zbl 1349.62001].
62D05 Sampling theory, sample surveys
94A62 Authentication, digital signatures and secret sharing
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