Adaptive spectral density estimation by model selection under local differential privacy

Martin Kroll

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arXiv · 2010.04218

Adaptive spectral density estimation by model selection under local differential privacy

Martin Kroll

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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.

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Martin Kroll. 2020-10-08. Adaptive spectral density estimation by model selection under local differential privacy. https://arxiv.org/abs/2010.04218

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