Abstract

We develop plug-in estimators for locally differentially private semi-parametric estimation via spline wavelets. The approach leads to optimal rates of convergence for a large class of estimation problems that are characterized by (differentiable) functionals \Lambda(f) of the true data generating density f. The crucial feature of the locally private data Z_1,\dots, Z_n we generate is that it does not depend on the particular functional \Lambda (or the unknown density f) the analyst wants to estimate. Hence, the synthetic data can be generated and stored a priori and can subsequently be used by any number of analysts to estimate many vastly different functionals of interest at the provably optimal rate. In principle, this removes a long standing practical limitation in statistics of differential privacy, namely, that optimal privacy mechanisms need to be tailored towards the specific estimation problem at hand. This is a joint work with Thibault Randrianarisoa and Lukas Steinberger.