Current-status data arise when an event time is observed only through an indicator of whether it occurred before an examination time. This paper studies a nonparametric neural-network sieve maximum likelihood estimator of the conditional cumulative distribution function of the event time. Under Hölder smoothness assumptions, we establish an explicit convergence rate by combining approximation theory for rectified linear unit neural networks with empirical-process arguments. This result provides theoretical support for neural-network estimation and subsequent inference under current-status observation.

翻译：当前状态数据是指通过观察事件时间是否发生在检查时间之前的指标来获取的数据形式。本文研究了事件时间条件累积分布函数的非参数神经网络筛最大似然估计量。在 Hölder 光滑性假设下，我们结合修正线性单元神经网络的逼近理论与经验过程论证，建立了明确的收敛速率。该结果为基于当前状态观测的神经网络估计及后续推断提供了理论支持。