# Multivariate Mean Comparison under Differential Privacy

@article{Dunsche2021MultivariateMC, title={Multivariate Mean Comparison under Differential Privacy}, author={Martin Dunsche and Timothy J. Kutta and Holger Dette}, journal={ArXiv}, year={2021}, volume={abs/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…

## References

SHOWING 1-10 OF 24 REFERENCES

Comparing Population Means under Local Differential Privacy: with Significance and Power

- Computer ScienceAAAI
- 2018

This paper proposes LDP tests that inject noise into every user's data in the samples before collecting them, and draw conclusions with bounded type-I (significance level) and type-II errors (1 - power).

Revisiting Differentially Private Hypothesis Tests for Categorical Data

- Mathematics, Computer Science
- 2015

A modified equivalence between chi-squared tests and likelihood ratio tests is shown, more suited to hypothesis testing with privacy, and differentially private likelihood ratio and chi-Squared tests for a variety of applications on tabular data are developed.

Improved Differentially Private Analysis of Variance

- Computer Science, MathematicsProc. Priv. Enhancing Technol.
- 2019

It is shown that the F -statistic, the optimal test statistic in the public setting, is no longer optimal in the private setting, and a new test statistic F1 is developed with much higher statistical power, and this test is compared to the only previous work on private ANOVA testing.

Privacy-preserving statistical estimation with optimal convergence rates

- Mathematics, Computer ScienceSTOC '11
- 2011

It is shown that for a large class of statistical estimators T and input distributions P, there is a differentially private estimator AT with the same asymptotic distribution as T, which implies that AT (X) is essentially as good as the original statistic T(X) for statistical inference, for sufficiently large samples.

The structure of optimal private tests for simple hypotheses

- Computer Science, MathematicsSTOC
- 2019

Hypothesis testing plays a central role in statistical inference, and is used in many settings where privacy concerns are paramount. This work answers a basic question about privately testing simple…

General-Purpose Differentially-Private Confidence Intervals

- MathematicsArXiv
- 2020

This work develops two broadly applicable methods for private confidence-interval construction based on asymptotics and the parametric bootstrap, which applies "out of the box" to a wide class of private estimators and has good coverage at small sample sizes, but with increased computational cost.

Differentially Private Covariance Estimation

- Computer ScienceNeurIPS
- 2019

This work proposes a new epsilon-differentially private algorithm for computing the covariance matrix of a dataset that has lower error than existing state-of-the-art approaches, both analytically and empirically.

Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing

- MathematicsICML 2016
- 2016

Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about…

The Algorithmic Foundations of Differential Privacy

- Computer ScienceFound. Trends Theor. Comput. Sci.
- 2014

The preponderance of this monograph is devoted to fundamental techniques for achieving differential privacy, and application of these techniques in creative combinations, using the query-release problem as an ongoing example.

Differentially Private Nonparametric Hypothesis Testing

- MathematicsCCS
- 2019

This work studies differentially private tests of independence between a categorical and a continuous variable, and presents private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon signed-rank tests, as well as the parametric one-sample t-test.