April 2021 Optimal disclosure risk assessment
Federico Camerlenghi, Stefano Favaro, Zacharie Naulet, Francesca Panero
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Ann. Statist. 49(2): 723-744 (April 2021). DOI: 10.1214/20-AOS1975


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¯=n+λn, with λ>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 τ1 of sample unique records that are population uniques. In this paper, we first study nonparametric estimation of τ1 under the Poisson abundance model for sample records. We introduce a class of linear estimators of τ1 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 τ1 all of the way up to the sampling fraction (λ+1)1(logn)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 τ1, which allows us to show that: (i) (λ+1)1(logn)1 is the smallest possible sampling fraction for consistently estimating τ1; (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 τ1 under the Poisson abundance model and for a sampling fraction (λ+1)1<1/2.


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Federico Camerlenghi. Stefano Favaro. Zacharie Naulet. Francesca Panero. "Optimal disclosure risk assessment." Ann. Statist. 49 (2) 723 - 744, April 2021. https://doi.org/10.1214/20-AOS1975


Received: 1 February 2019; Revised: 1 April 2020; Published: April 2021
First available in Project Euclid: 2 April 2021

Digital Object Identifier: 10.1214/20-AOS1975

Primary: 62G05
Secondary: 62C20

Keywords: Disclosure risk assessment , microdata sample , nonparametric inference , optimal minimax procedure , Poisson abundance model , polynomial approximation

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.49 • No. 2 • April 2021
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