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

Understand

This work provides tight upper- and lower-bounds for the problem of mean estimation under $\epsilon$-differential privacy in the local model, when the input is composed of $n$ i.i.d.

• drawn samples from a normal distribution with variance $\sigma$.
• Our algorithms result in a $(1-\beta)$-confidence interval for the underlying distribution's mean $\mu$ of length $\tilde O\left( \frac{\sigma \sqrt{\log(\frac 1 \beta)}}{\epsilon\sqrt n} \right)$.
• In addition, our algorithms leverage binary search using local differential privacy for quantile estimation, a result which may be of separate interest.