AI 中文总结
本文针对离散时间半马尔可夫系统，提出基于多条轨迹的非参数可靠性推断方法，区分年龄限制与日历截断，建立渐近正态性并给出诊断与选择规则，经数值和真实数据验证。
AI 中文摘要
我们针对在共同固定时间范围内观测到的独立轨迹，发展了离散时间半马尔可夫系统可靠性指标的非参数推断。通过将物理状态与向后递推时间相结合，在观测到的年龄范围内得到一个有限耦合马尔可夫表示。我们将由此产生的受年龄限制的失效或退出时间与日历截断区分开来，因为这两个有限时间范围的量仅在特殊情况下才一致。该框架涵盖了受限阶乘矩和矩特征、日历截断的失效时间汇总以及命中时间的离散时间强度。在明确的逐行暴露条件下，我们建立了经验初始分布、所需转移行和相应插件泛函的强一致性和联合渐近正态性。高斯随机矩阵表示给出了逐点和联合协方差公式、同时置信包络、针对线性汇总的Wald程序以及曲率调整的高斯近似。我们分别开发了限制诊断和基于暴露、边界交互和嵌套时间范围稳定性的目标特定时间范围选择规则。数值实验评估了推断公式和诊断方法，而来自欧洲血液与骨髓移植组的完整案例说明报告了日历截断的失效时间汇总和有限维命中强度。
英文摘要
We develop nonparametric inference for reliability indicators of discrete-time semi-Markov systems from independent trajectories observed over a common fixed horizon. Augmenting the physical state by the backward recurrence time yields a finite coupled Markov representation on the observed age range. We distinguish the resulting age-restricted failure-or-exit time from calendar truncation, since these two finite-horizon quantities coincide only in special cases. The framework covers restricted factorial moments and moment characteristics, calendar-truncated failure-time summaries, and the discrete-time intensity of the hitting time. Under explicit row-exposure conditions, strong consistency and joint asymptotic normality are established for the empirical initial law, the required transition rows and the corresponding plug-in functionals. The Gaussian random-matrix representation gives pointwise and joint covariance formulas, simultaneous confidence envelopes, Wald procedures for linear summaries, and curvature-adjusted Gaussian approximations. Restriction diagnostics and a target-specific horizon-selection rule based on exposure, boundary interaction and nested-horizon stability are developed separately. Numerical experiments assess the inferential formulas and the diagnostics, while a complete-case illustration from the European Group for Blood and Marrow Transplantation reports calendar-truncated failure-time summaries and finite-dimensional hitting intensities.
Comments39 pages, 2 figures
