zbMATH — the first resource for mathematics

Cramer-Rao lower bounds of variance for estimating two proportions and their overlap by using two decks of cards. (English) Zbl 1365.62035
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, 353-385 (2016).
Summary: In this chapter, we show that the three estimators proposed by the authors [Stat. Probab. Lett. 83, No. 1, 399–409 (2013; Zbl 1341.62044)] attain the lower bounds of variance at equal protection of respondents. A comparison of a range restricted estimate with an unrestricted estimate is also given. The findings are supported with an example using real data.
For the entire collection see [Zbl 1349.62001].

62D05 Sampling theory, sample surveys
62F10 Point estimation
Full Text: DOI