Abstract: We consider the problem of estimating a regression function from anonymized data in the framework of local differential privacy. We propose a novel partitioning estimate of the regression function, derive a rate of convergence for the excess prediction risk over Hölder classes, and prove a matching lower bound. In contrast to the existing literature on the problem, the so-called strong density assumption on the design distribution is obsolete.

Key words and phrases: Local differential privacy, minimax lower bound, nonparametric regression, partitioning estimate, rate of convergence.