We consider the estimation of the cumulative hazard function, and equivalently the distribution function, with censored data under a setup that preserves the privacy of the survival database. This is done through a $\alpha$-locally differentially private mechanism for the failure indicators and by proposing a non-parametric kernel estimator for the cumulative hazard function that remains consistent under the privatization. Under mild conditions, we also prove lowers bounds for the minimax rates of convergence and show that estimator is minimax optimal under a well-chosen bandwidth.

翻译：本文考虑在保护生存数据库隐私的设置下，基于删失数据对累积风险函数（等价于分布函数）进行估计。我们通过引入针对失效指标的α-局部差分隐私机制，并提出一种在私有化条件下保持一致性的累积风险函数非参数核估计量来实现这一目标。在温和条件下，我们还证明了极小化极大收敛速度的下界，并表明该估计量在恰当选择的带宽下达到极小化极大最优性。