Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanism

Randomized response is one of the oldest and most well-known methods for analyzing confidential data. However, its utility for differentially private hypothesis testing is limited because it cannot achieve high privacy levels and low type I error rates simultaneously. In this article, we show how to overcome this issue with the subsample and aggregate technique. The result is a broadly applicable method that can be used for both frequentist and Bayesian testing. We illustrate the performance of our proposal in two scenarios: goodness-of-fit testing for linear regression models and nonparametric testing of a location parameter.