Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates
This work provides theoretical guarantees for survival analysis methods, which is important for researchers and practitioners in statistics and machine learning dealing with censored data, though it appears incremental as it builds on existing estimators.
The paper tackles the problem of establishing error bounds for nonparametric survival probability estimators based on Kaplan-Meier, nearest neighbor, and kernel methods in metric spaces, achieving the first nonasymptotic error bounds that imply strong consistency rates and match an existing lower bound up to a log factor.
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.