2021/10/15 by Martin Dunsche, Dunsche, Martin, Tim Kutta +3 · 1 citation
Mathematics · #Statistical Methods and Inference #Statistical Methods and Bayesian Inference #Survey Sampling and Estimation Techniques
paper · pdf · doi:10.48550/arxiv.2110.07996
The comparison of multivariate population means is a central task of statistical inference. While statistical theory provides a variety of analysis tools, they usually do not protect individuals' privacy. This knowledge can create incentives for participants in a study to conceal their true data (especially for outliers), which might result in a distorted analysis. In this paper we address this problem by developing a hypothesis test for multivariate mean comparisons that guarantees differential privacy to users. The test statistic is based on the popular Hotelling's t2-statistic, which has a natural interpretation in terms of the Mahalanobis distance. In order to control the type-1-error, we present a bootstrap algorithm under differential privacy that provably yields a reliable test decision. In an empirical study we demonstrate the applicability of this approach.