Nonparametric differentially private confidence intervals for the median
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Published version
Date
2022-06-28
Authors
Drechsler, Jörg
Globus-Harris, Ira
Mcmillan, Audra
Sarathy, Jayshree
Smith, Adam
Version
Published version
OA Version
Citation
J. Drechsler, I. Globus-Harris, A. Mcmillan, J. Sarathy, A. Smith. 2022. "Nonparametric Differentially Private Confidence Intervals for the Median" Journal of Survey Statistics and Methodology, Volume 10, Issue 3, pp.804-829. https://doi.org/10.1093/jssam/smac021
Abstract
Differential privacy is a restriction on data processing algorithms that provides strong confidentiality guarantees for individual records in the data. However, research on proper statistical inference, that is, research on properly quantifying the uncertainty of the (noisy) sample estimate regarding the true value in the population, is currently still limited. This article proposes and evaluates several strategies to compute valid differentially private confidence intervals for the median. Instead of computing a differentially private point estimate and deriving its uncertainty, we directly estimate the interval bounds and discuss why this approach is superior if ensuring privacy is important. We also illustrate that addressing both sources of uncertainty—the error from sampling and the error from protecting the output—simultaneously should be preferred over simpler approaches that incorporate the uncertainty in a sequential fashion. We evaluate the performance of the different algorithms under various parameter settings in extensive simulation studies and demonstrate how the findings could be applied in practical settings using data from the 1940 Decennial Census.
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License
Copyright The Author(s) 2022. Published by Oxford University Press on behalf of the American Association for Public Opinion Research. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com