  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.
