Parametric inference for time‐to‐failure in multi‐state semi‐Markov models: A comparison of marginal and process approaches
Parametric inference for time‐to‐failure in multi‐state semi‐Markov models: A comparison of marginal and process approaches
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多状态半马尔可夫模型中时间失效的参数推断：边际方法和过程方法的比较
DOI：
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发表时间：
2011
期刊：
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通讯作者：
V. Nair
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文献类型：
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作者：
Yang Yang;V. Nair
在许多应用程序中，一些感兴趣的事件（通常称为“失败”）的时间是潜在随机过程的终点。本文考虑了可以用多状态模型来表征的过程，特别是渐进的半马尔可夫过程。在此框架下，作者研究了两种方法对TTF分布进行推断的估计和预测效率。第一种是仅基于TTF数据的传统方法。第二种方法是利用多态数据中的所有信息来估计底层参数，然后对TTF进行推断。后一种推断对于面板数据可能很复杂（涉及间隔和右审查），因此量化效率增益以确定额外的复杂性是否值得付出努力是很重要的。作者主要关注状态逗留时间的伽马分布，因为它们在卷积下是封闭的。并简要讨论了具有这种性质的逆高斯情形的结果。加拿大统计杂志39:537-555；2011©2011加拿大统计学会
In many applications, the time to some event of interest (generically called “failure”) is the end point of an underlying stochastic process. This article considers processes that can be characterized by multi‐state models, specifically progressive semi‐Markov processes. Under this framework, the authors examine estimation and prediction efficiencies of two approaches for making inference about the time‐to‐failure (TTF) distribution. The first is the traditional approach based on just TTF data. The second uses all the information in the multi‐state data to estimate the underlying parameters and then makes inference about the TTF. The latter inference can be complex with panel data (involving interval and right censoring), so it is important to quantify the efficiency gains to determine if the additional complexity is worth the effort. The authors focus mostly on gamma distributions for state sojourn times because they are closed under convolution. Results for the inverse Gaussian case which shares this property are also briefly discussed. The Canadian Journal of Statistics 39: 537–555; 2011 © 2011 Statistical Society of Canada