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Incredibly efficient use of a negative hypergeometric distribution in randomized response techniques. (English) Zbl 1365.62033
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, 443-469 (2016).
Summary: In this chapter, a new randomized response device is proposed based on the use of a pair of negative hypergeometric distribution when estimating the proportion of persons in a population possessing a sensitive characteristic in a population. The proposed resultant estimator is found to be more efficient than the recent model studied by S. Singh and S. A. Sedory [Metron 71, No. 1, 3–8 (2013; Zbl 1302.62023)], and hence in turn remains more efficient than the S. L. Warner [J. Am. Stat. Assoc. 60, No. 309, 63–69 (1965; Zbl 1298.62024)], the A. Y. C. Kuk [Biometrika 77, No. 2, 436–438 (1990; Zbl 0711.62011)], and the N. S. Manga [J. R. Stat. Soc., Ser. B 56, No. 1, 93–95 (1994; Zbl 0788.62013)] estimators under the same situations investigated by Singh and Sedory [loc. cit.].
For the entire collection see [Zbl 1349.62001].

MSC:
62D05 Sampling theory, sample surveys
94A62 Authentication, digital signatures and secret sharing
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