We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for conditional CDF estimation. Our proof strategy also yields nonasymptotic guarantees for nearest neighbor and kernel variants of the Nelson-Aalen cumulative hazards estimator. We experimentally compare these methods on four datasets. We find that for the kernel survival estimator, a good choice of kernel is one learned using random survival forests.
翻译:我们为位于卡普兰-麦尔(Kaplan-Meier)的近邻和内核生存概率测算器建立了第一个非补救性误差界限。 我们的误差意味着这些非参数测算器具有很强的一致性, 并且, 直至一个日志系数, 匹配现有的有条件的CDF估计下限。 我们的校对策略也为Nelson-Aalen(Nelson-Aalen)累积危险测算器的近邻和内核变体提供非补救性担保。 我们在四个数据集上对这些方法进行了实验性比较。 我们发现,对于内核生存测算器来说, 正确的内核选择是使用随机生存森林学习的。