OPTIMAL DISCLOSURE RISK ASSESSMENT

• 成果类型: Article
• 署名作者: Camerlenghi, Federico; Favaro, Stefano; Naulet, Zacharie; Panero, Francesca
• 署名单位: University of Milano-Bicocca; University of Turin; Universite Paris Saclay; University of Oxford
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS1975
• 发表日期: 2021
• 页码: 723-744

摘要

Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Consider a microdata sample of size n from a finite population of size (n) over bar n = n + lambda n, with lambda > 0, such that each sample record contains two disjoint types of information: identifying categorical information and sensitive information. Any decision about releasing data is supported by the estimation of measures of disclosure risk, which are defined as discrete functionals of the number of sample records with a unique combination of values of identifying variables. The most common measure is arguably the number tau(1) of sample unique records that are population uniques. In this paper, we first study nonparametric estimation of tau(1) under the Poisson abundance model for sample records. We introduce a class of linear estimators of tau(1) that are simple, computationally efficient and scalable to massive datasets, and we give uniform theoretical guarantees for them. In particular, we show that they provably estimate tau(1) all of the way up to the sampling fraction (lambda + 1)(-1) proportional to (log n)(-1), with vanishing normalized mean-square error (NMSE) for large n. We then establish a lower bound for the minimax NMSE for the estimation of tau(1), which allows us to show that: (i) (lambda + 1)(-1) proportional to (log n)(-1) is the smallest possible sampling fraction for consistently estimating tau(1); (ii) estimators' NMSE is near optimal, in the sense of matching the minimax lower bound, for large n. This is the main result of our paper, and it provides a rigorous answer to an open question about the feasibility of nonparametric estimation of tau(1) under the Poisson abundance model and for a sampling fraction (lambda+ 1)(-1) < 1/2.