The semi‐Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end‐point of the support of the censoring time is strictly less than the right end‐point of the support of the semi‐Markov kernel, the transition probability of the semi‐Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi‐Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study. The Canadian Journal of Statistics 41: 237–256; 2013 © 2013 Statistical Society of Canada

中文翻译：

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半马尔可夫模型下右删失观测的估计。

对于多状态事件的分析，半马尔可夫过程通常提供比经典马尔可夫过程更好的框架。本文的目的是双重的。首先，我们证明了在存在右删失的情况下，当删失时间的支持度的右端点严格小于半马尔可夫核的支持度的右端点时，半马尔可夫核的转移概率-马尔可夫过程是不可识别的，文献中提出的估计量总体上是不一致的。我们根据删失数据推导出所有可达到的转移概率值的集合，并且我们提出了使用该集合的转移概率的非参数推理程序。第二，构建置信带的传统方法不适用于半马尔可夫核和逗留时间分布。我们提出了新的扰动重采样方法来构建这些置信带。在构造中探索了不同的权重和变换。我们使用模拟来检查我们的建议，并用最近癌症幸存者研究的住院数据来说明它们。加拿大统计杂志41：237-256；2013 © 2013 加拿大统计学会