Multivariate Mean Comparison under Differential Privacy
Abstract
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 -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.
Cite
@article{arxiv.2110.07996,
title = {Multivariate Mean Comparison under Differential Privacy},
author = {Martin Dunsche and Tim Kutta and Holger Dette},
journal= {arXiv preprint arXiv:2110.07996},
year = {2021}
}