區間設限資料之統計推論-文獻回顧

Abstract

在此論文中,我們回顧區間設限資料的推論問題,為呈現概 念的建構原則,亦簡述其它類型的不完整資料.論文分兩大部份, 一部份為無母數估計,另一部份為迴歸分析.我們回顧了兩類的 無母數估計法,其中自我一致演算法可視為動差法的延伸.另一 方法為無母數最大概似估計法.我們介紹三種較廣泛使用的迴歸 模型: 包含比例風險模型,加速失敗模型和比例勝算模型.推論 的困難度在於模式存在未知函數,需要利用平滑的技巧處理之. 本論文以介紹點估計的概念為主,並未涵蓋如何由分佈理論推導 信賴區間與統計檢定問題.

We review inference methods for analyzing incomplete data with focus on interval censored data. For nonparametric analysis, two estimation approaches are examined. Self-consistency can be viewed as an extension of the method of moment by imputing incomplete information by its expected value. The other is the nonparametric likelihood estimation. We also introduce three popular regression models, namely the proportional hazards model, accelerated failure time model, and proportional odds model. These models contain unknown nuisance functions and different smoothing techniques are employed to handle them in the estimation procedure. The thesis focuses on point estimation so that second ordered properties are not investigated.