串行存活資料之相關性分析

Abstract

在許多應用中，探討兩變數的相關性是一項重要課題。本論文針對串行存活資料， 針對兩段間隔時間討論估計相關性的推論方法。在文獻回顧中，我們介紹了全面與局部 相關性指標、兩個有用的推論方法與串行資料的相依設限問題和估計方法。我們聚焦在 以 V-統計量估計兩段間隔時間的推論問題，除了介紹我們提出的方法以外，並以模擬檢 驗其表現。最後我們以一組資料示範如何運用論文所介紹的方法分析關聯性。

Association analysis plays a key in many scientific applications. Kendall’s tau is a rank-invariant association measure which is useful because of its robustness property. In this thesis, we utilize the idea of V-statistics in the estimation of Kendall's tau for serial gap time data. The bivariate estimator by Lin, Sun and Ying (1999), which can handle the problem of induced dependent censoring, is adopted as the plug-in estimator in the integral form. We examine how the tail problem affects the estimation via simulations. We also apply the method to analyze a real dataset for illustrative purposes.