A0479
Title: Locally differentially private drift parameter estimation for iid paths of diffusion processes
Authors: Arnaud Gloter - Universite d Evry Val d Essonne (France) [presenting]
Chiara Amorino - Universite du Luxembourg (Luxembourg)
Helene Halconruy - ESILV (France)
Abstract: The problem of parametric drift estimation is addressed for $N$ discretely observed iid SDEs, considering the additional constraints that only privatized data can be published and used for inference. The concept of local differential privacy is formally introduced for a system of stochastic differential equations. The aim is to estimate the drift parameter by proposing a contrast function based on a pseudo-likelihood approach. A suitably scaled Laplace noise is incorporated to satisfy the privacy requirement. One main result consists of deriving explicit conditions on the privacy level for which the associated estimator is proven to be consistent. The asymptotic behavior of the estimator is also derived, and how the rate of convergence is linked to the privacy level is determined. This holds true as the discretization step approaches zero and the number of processes $N$ tends to infinity.
