Admissible and optimal estimation in finite population sampling under randomized response models. (English) Zbl 1365.62050

Sengupta, S.

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, 91-104 (2016).

Summary: We consider the problem of unbiased estimation of finite population mean (or proportion) related to a sensitive character under some randomized response models covering different randomized response plans and present a comprehensive review of various nonexistence, admissibility, and optimality results on the problem paralleling those for direct surveys.
For the entire collection see [Zbl 1349.62001].

MSC:

62D05	Sampling theory, sample surveys
62C15	Admissibility in statistical decision theory

Keywords:

admissibility; optimality; population mean; population proportion; randomized response; sampling strategy; super-population model; unbiased estimator; variance estimation