Multivariate Mean Comparison Under Differential Privacy

• Published in: Privacy in Statistical Databases Vol. 13463; pp. 31 - 45
• Main Authors: Dunsche, Martin, Kutta, Tim, Dette, Holger
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2022; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Differential privacy; Private bootstrap; Private testing
• ISBN: 9783031139444; 3031139445
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-031-13945-1_3

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 $$t^2$$ -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.