Multiple Imputation for Parametric Inference Under a Differentially Private Laplace Mechanism

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.