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Estimating sensitive population proportion by generating randomized response following direct and inverse hypergeometric distribution. (English) Zbl 1365.62031
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, 427-441 (2016).
Summary: We consider estimating the proportion of people containing sensitive attributes like habitual drunkenness, drug addiction, reckless car driving, evading the tax liabilities, etc., in a given community. Following the pioneering work of S. Singh and S. A. Sedory [Metron 71, No. 1, 3–8 (2013; Zbl 1302.62023)], we examine the effectiveness of generating randomized responses by negative hypergeometric distribution in respect to generating randomized responses by direct hypergeometric distribution. We consider sampling of respondents by general sampling schemes having the positive inclusion probabilities for single and paired population units. Essential theoretical derivations for unbiased estimator, variance and variance estimators are presented here. We perform a numerical illustration for compaiison purpose which support the usefulness of Singh and Sedory’s [loc. cit.] negative hypergeometric approach.
For the entire collection see [Zbl 1349.62001].
62D05 Sampling theory, sample surveys
94A62 Authentication, digital signatures and secret sharing
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