Theoretical Convergence Rates Established for Neural Networks with Current-Status Data
Researchers have derived explicit convergence rates for a nonparametric neural-network sieve maximum likelihood estimator applied to current-status data, a setting where event times are only partially observed. The work combines approximation theory for ReLU neural networks with empirical-process methods under Hölder smoothness assumptions. The results provide formal theoretical guarantees for using neural networks in survival analysis and subsequent statistical inference under this type of censored observation.
A preprint posted to arXiv on June 8, 2026 presents theoretical analysis of neural-network-based estimation for current-status data, a common structure in survival and reliability studies where an event time is known only to have occurred before or after a single examination time. The authors propose a nonparametric sieve maximum likelihood estimator of the conditional cumulative distribution function of the event time, implemented via rectified linear unit (ReLU) neural networks. By imposing Hölder smoothness conditions on the underlying function class, they derive explicit convergence rates that characterize how quickly the estimator approaches the true distribution as sample size grows. The proof strategy integrates neural-network approximation theory with empirical-process arguments, two methodological pillars that have been increasingly combined in modern nonparametric statistics. The findings offer rigorous theoretical backing for practitioners who wish to apply neural networks to interval-censored or current-status survival data, and they lay groundwork for valid downstream inference procedures in such settings.
What's missing
The preprint does not report simulation studies or real-data experiments that would illustrate finite-sample performance of the estimator, leaving a gap between the asymptotic theory and practical guidance. Peer review has not yet been completed.
What different sources said
- arXiv cs.LGCenter
Convergence Rates for Neural-Network Estimation with Current-Status Data
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