Eliciting information on sensitive features: block total response technique and related inference. (English) Zbl 1365.62041

Nandy, K.; Marcovitz, M.; Sinha, B. K.

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, 317-329 (2016).

Summary: Randomized response technique was first introduced and popularized by S. L. Warner [J. Am. Stat. Assoc. 60, No. 309, 63–69 (1965; Zbl 1298.62024)]. Since then, survey sampling theoreticians and practitioners have contributed significantly in this area of survey methodological research. The idea is to be able to elicit a “truthful” response on sensitive feature(s) from the sampled respondents (of a finite labeled population of respondents), so that eventually the population mean of the sensitive feature can be unbiasedly stimated. Toward this, a novel technique was introduced by D. Raghavarao and W. T. Federer [J. R. Stat. Soc., Ser. B. 41, 40–45 (1979; Zbl 0453.62011)] and it was tenned “Block Total Response” (BTR) technique. We undertake various meaningful versions/generalizations of the BTR technique, after a brief review of the literature in this direction. In the process, we also introduce empirical Bayes estimators.
For the entire collection see [Zbl 1349.62001].

MSC:

62D05	Sampling theory, sample surveys
94A62	Authentication, digital signatures and secret sharing
62K10	Statistical block designs
62F05	Asymptotic properties of parametric tests

Keywords:

survey sampling; sensitive feature; regular feature; randomized response technique; block total response technique; balanced incomplete block design; binary proper equireplicate block design; empirical Bayes estimators