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.

翻译：我们根据本地差异隐私研究光谱密度估计。 匿名是通过脱轨实现的, 然后是Laplace 扰动。 我们从一组候选人估计标准中选择了我们的估计值, 使用一个惩罚性对比标准。 这个估计值显示, 达到与候选数中最佳估计值几乎相同的趋同率。 证据的一个关键成分是最近的结果, 从亚氧基:1903. 05. 964获得的亚爆炸性随机变量中, 四方形式集中。 我们在一个小型模拟研究中展示了我们的结论 。