Multiple Imputation for Parametric Inference Under a Differentially Private Laplace Mechanism
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2019-05-09
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Martin Klein and Bimal Sinha, Multiple Imputation for Parametric Inference Under a Differentially Private Laplace Mechanism, Research Report Series, 2019, https://www.census.gov/srd/papers/pdf/RRS2019-05.pdf
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This is a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law." in either case, put on a public domain creative commons license.
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Abstract
In this paper we consider the scenario where continuous microdata have been noise infused
using a differentially private Laplace mechanism for the purpose of statistical disclosure control.
We assume the original data are independent and identically distributed, having distribution within
a parametric family of continuous distributions. We employ a modification of the standard Laplace
mechanism that allows the range of the original data to be unbounded. We propose methodology
to analyze the noise infused data using multiple imputation. This approach allows the data user to
analyze the released data as if it were original, i.e., not noise infused, and then to obtain inference
that accounts for the noise infusion mechanism using standard multiple imputation combining
formulas. Methodology is presented for univariate data, and some simulation studies are presented
to evaluate the performance of the proposed method. An extension of the proposed methodology
to multivariate data is also presented.