Locally Private Mean Estimation: Z-test and Tight Confidence Intervals

This work provides tight upper-and lower-bounds for the problem of mean estimation under differential privacy in the local-model, when the input is composed of n i.i.d. drawn samples from a Gaussian. Our algorithms re-sult in a (Formula Presented)-confidence interval for the underlying distribution's mean µ of length (Formula Presented). In addition, our algorithms leverage on binary search using local differential privacy for quantile estima-tion, a result which may be of separate inter-est. Moreover, our algorithms have a match-ing lower-bound, where we prove that any one-shot (each individual is presented with a single query) local differentially private al-gorithm must return an interval of length (Formula Presented).