有序事件之無母數存活分析

Abstract

在論文中我們針對連續事件的間隔時探討聯合分配函數的推論方法。文獻中對這類的問題有兩個不同的處理方式。傳統的方法以隨機過程的角度切入，並對狀態的轉移率做模式的假設。近十年來有學者嘗試用多維存活分析的技巧處理此類的問題。 我們選出兩種無母數的估計方法並透過模擬比較其差異。第一個方法由Frydman 所提出 (1992)，在馬可夫模型下建構無母數最大概似估計量。第二個方法是由 Wang and Wells (1998) 年提出，將感興趣的二維存活函數拆解成乘積極限 (product limit) 的形式，並透過加權的方法處理相關設限的問題。後者不需要任何模型假設。 透過模擬我們驗證了無母數最大概似估計量在資料符合假設時具有較好的效度，然而假設錯誤時則會出現偏誤。第二個方法因未用到任何模型的假設，所較為穩健。

Consider nonparametric analysis for successive events in which the joint survival function of the duration times is of major interest. Such a phenomenon is usually investigated under the framework of stochastic processes in which the transition rates are modeled by Markov-related properties. In the past decade, some authors have applied techniques of multivariate survival analysis to handle the problem. In the thesis, we compare two different nonparametric estimators which are constructed based on different ideas. One estimator was proposed by Frydman (1992) who considered nonparametric MLE under a Markov assumption. The other estimator was proposed by Wang and Wells (1998) who suggested to decompose the target function in terms of estimable quantities. The latter does not make any model assumption. Via simulations, we want to verify our conjecture. Briefly speaking, we suspect that the NPMLE will be more efficient if the Markov property holds but will be biased if this assumption is violated. On the other hand, the estimator proposed by Wang and Wells (1998) should be more robust since it does not require any model assumption.