Adaptive spectral density estimation by model selection under local differential privacy

TL;DR

This paper introduces an adaptive spectral density estimation method under local differential privacy, using model selection and penalized contrast to achieve near-optimal convergence rates, supported by theoretical analysis and simulations.

Contribution

It proposes a novel adaptive estimator for spectral density under local differential privacy, combining truncation, Laplace noise, and model selection with theoretical guarantees.

Findings

Estimator attains near-optimal convergence rates.

Method effectively balances privacy and estimation accuracy.

Simulation results validate theoretical findings.

Abstract

We study spectral density estimation under local differential privacy. Anonymization is achieved through truncation followed by Laplace perturbation. We select our estimator from a set of candidate estimators by a penalized contrast criterion. This estimator is shown to attain nearly the same rate of convergence as the best estimator from the candidate set. A key ingredient of the proof are recent results on concentration of quadratic forms in terms of sub-exponential random variables obtained in arXiv:1903.05964. We illustrate our findings in a small simulation study.