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：我们考虑在保护生存数据库隐私的条件下，利用删失数据对累积风险函数（等价于分布函数）进行估计。通过引入针对失效指标的α-局部差分隐私机制，并构建在隐私化处理下仍保持一致性的累积风险函数非参数核估计量，实现了该目标。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具有极小化极大最优性。