{"ID":2880773,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.13969","arxiv_id":"2508.13969","title":"Towards multi-purpose locally differentially-private synthetic data release via spline wavelet plug-in estimation","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 $Λ(f)$ 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 $Λ$ (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.","short_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 $Λ(f)$ of the true data generating density $f$. The crucial...","url_abs":"https://arxiv.org/abs/2508.13969","url_pdf":"https://arxiv.org/pdf/2508.13969v2","authors":"[\"Thibault Randrianarisoa\",\"Lukas Steinberger\",\"Botond Szabó\"]","published":"2025-08-19T16:00:14Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}