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Abstract:
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Differential privacy (DP) mechanisms protect individual-level information by introducing randomness into the statistical analysis procedures. While there are now many DP tools for various statistical problems, many focus on providing point estimates. However, in statistical inference, it is also required to understand the sampling distribution rather than having only a point estimate. We propose a DP bootstrap procedure which releases multiple samples at a comparable privacy cost. Our method is widely applicable to incorporate arbitrary existing DP mechanisms, and does not require any parametric assumptions on the data. We develop a novel statistical procedure to correctly infer the sampling distribution of the DP point estimate based on the DP bootstrap, using techniques related to deconvolution of probability measures. This allows us to derive accurate confidence intervals. Through simulations and real-world experiments, we show the advantage of our method compared to existing methods.
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