Comparison Of Two Mean Vectors Under Differential Privacy For High-Dimensional Data

The multivariate hypothesis testing problem is a more interesting task of the statistical inference for high-dimensional data nowadays, in which the dimension of the observation vectors is diverging and could even be larger than the sample size. However, in many applications of multivariate hypotheses problems, the data are highly sensitive and require privacy protection. Here we consider a private non-parametric projection test for the comparison of the high-dimensional multivariate mean vectors that guarantees strong differential privacy. The empirical evidence shows that the non-parametric projection test under differential privacy gives accurate inference under the null hypothesis and a higher power under the local alternative hypothesis.