# Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates

arXiv: https://arxiv.org/abs/1905.05285 · HTML: https://mlsanity.com/paper/1905.05285/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2019.

## Built on by (most cited first, 8 of 8)

- [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024)
- [Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee](https://mlsanity.com/paper/2206.10477/) (2022)
- [Survival In-Context: Amortized Bayesian Survival Analysis via Prior-Fitted Networks](https://mlsanity.com/paper/2603.29475/) (2026)
- [Conformal Prediction Under Generalized Covariate Shift with Posterior Drift](https://mlsanity.com/paper/2502.17744/) (2025)
- [Conditional Mean and Variance Estimation via textitk-NN Algorithm with Automated Variance Selection](https://mlsanity.com/paper/2402.01635/) (2024)
- [Conditional Outcome Equivalence: A Quantile Alternative to CATE](https://mlsanity.com/paper/2410.12454/) (2024)
- [Area-norm COBRA on Conditional Survival Prediction](https://mlsanity.com/paper/2309.00417/) (2023)
- [Metaparametric Neural Networks for Survival Analysis](https://mlsanity.com/paper/2110.06610/) (2021)

## Abstract (arXiv)

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.