Electronic Journal of Statistics

A criterion for privacy protection in data collection and its attainment via randomized response procedures

Jichong Chai and Tapan K. Nayak

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Randomized response (RR) methods have long been suggested for protecting respondents’ privacy in statistical surveys. However, how to set and achieve privacy protection goals have received little attention. We give a full development and analysis of the view that a privacy mechanism should ensure that no intruder would gain much new information about any respondent from his response. Formally, we say that a privacy breach occurs when an intruder’s prior and posterior probabilities about a property of a respondent, denoted $p$ and $p_{*}$, respectively, satisfy $p_{*}<h_{l}(p)$ or $p_{*}>h_{u}(p)$, where $h_{l}$ and $h_{u}$ are two given functions. An RR procedure protects privacy if it does not permit any privacy breach. We explore effects of $(h_{l},h_{u})$ on the resultant privacy demand, and prove that it is precisely attainable only for certain $(h_{l},h_{u})$. This result is used to define a canonical strict privacy protection criterion, and give practical guidance on the choice of $(h_{l},h_{u})$. Then, we characterize all privacy satisfying RR procedures and compare their effects on data utility using sufficiency of experiments and identify the class of all admissible procedures. Finally, we establish an optimality property of a commonly used RR method.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 4264-4287.

Received: February 2018
First available in Project Euclid: 15 December 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62D05: Sampling theory, sample surveys
Secondary: 62B15: Theory of statistical experiments

admissibility Bayes factor data utility privacy breach sufficiency of experiments transition probability matrix

Creative Commons Attribution 4.0 International License.


Chai, Jichong; Nayak, Tapan K. A criterion for privacy protection in data collection and its attainment via randomized response procedures. Electron. J. Statist. 12 (2018), no. 2, 4264--4287. doi:10.1214/18-EJS1508. https://projecteuclid.org/euclid.ejs/1544842902

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