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On the universal consistency of histograms anonymised by a randomised response technique

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  • Kroll, Martin

Abstract

The purpose of this short letter is to provide sufficient conditions for universal consistency (both pointwise and with respect to the L1-error) of density estimators under local differential privacy. As the object of study we consider the well-known histogram estimator anonymised by a randomised response technique in a multivariate setup. The universal consistency of this method has not been studied yet and, in contrast to existing work on other privacy mechanisms, we make the dependence on the privacy level in the conditions ensuring universal consistency explicit. Besides the stronger assumptions on the bandwidth parameter to obtain universal consistency, this approach also allows to record the effective reduction of the sample size present under local differential privacy.

Suggested Citation

  • Kroll, Martin, 2022. "On the universal consistency of histograms anonymised by a randomised response technique," Statistics & Probability Letters, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:stapro:v:185:y:2022:i:c:s0167715222000347
    DOI: 10.1016/j.spl.2022.109420
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    References listed on IDEAS

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    1. John C. Duchi & Michael I. Jordan & Martin J. Wainwright, 2018. "Minimax Optimal Procedures for Locally Private Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 182-201, January.
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