A concise theory of randomized response techniques for privacy and confidentiality protection. (English) Zbl 1365.62042

Nayak, T. K.; Adeshiyan, S. A.; Zhang, C.

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, 273-286 (2016).

Summary: A variety of randomized response (RR) procedures for privacy and confidentiality protection have been proposed, studied, and compared in the literature. We describe statistically relevant attributes of RR mechanisms and use those to duly organize and unify existing estimation theories for diverse RR methods. Any RR procedure can be characterized by its transition probability matrix \(P\), as it determines all statistical properties of the procedure. In RR surveys, \(P\) is fixed, but in post-randomization for confidentiality protection, \(P\) may depend on the original data. This affects statistical inferences significantly. We also review some optimality results in the comparison of RR surveys of a binary variable, based on both privacy protection and statistical efficiency.
For the entire collection see [Zbl 1349.62001].

MSC:

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

Keywords:

categorical variable; post-randomization; random transformation; sampling design; transition probability matrix; unbiased estimation; variance inflation