# Multivariate Mean Comparison under Differential Privacy

arXiv: https://arxiv.org/abs/2110.07996 · HTML: https://mlsanity.com/paper/2110.07996/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2021.

## Built on by (most cited first, 1 of 1)

- [Sample-optimal learning of quantum states using gentle measurements](https://mlsanity.com/paper/2505.24587/) (2025)

## Abstract (arXiv)

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.