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：我们考虑在生存数据库隐私保护的设定下，基于删失数据估计累积风险函数（等价于分布函数）。通过引入失效指标的$\alpha$-局部差分隐私机制，并提出一种在隐私化条件下保持相合性的非参数核估计量，实现了累积风险函数的估计。在温和条件下，我们证明了极小化最大收敛速率的下界，并表明在适当选择的带宽下该估计量具有极小化最大最优性。