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

TL;DR

This paper introduces a new differentially private hypothesis testing method combining subsample and aggregate techniques with randomized response, enabling high privacy and low error rates in various statistical tests.

Contribution

It presents a novel general-purpose approach that improves privacy-utility trade-offs for both frequentist and Bayesian hypothesis testing.

Findings

Effective in goodness-of-fit testing for linear regression

Applicable to nonparametric tests like Wilcoxon and Kruskal-Wallis

Achieves high privacy levels with low type I error rates

Abstract

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 general-purpose method that can be used for both frequentist and Bayesian testing. {{We illustrate the performance of our proposal in three scenarios: goodness-of-fit testing for linear regression models, nonparametric testing of a location parameter with the Wilcoxon test, and the nonparametric Kruskal-Wallis test.