線性轉換模型之統計推論

Abstract

線性轉換模型是相當彈性的半母數迴歸模型。倖存分析常見的Cox模型與Odds模型，皆是線性轉換模型的特例。近年來許多研究針對線性轉換模型提出半母數推論方法，一套分析方法卻有廣泛的應用價值，是其吸引人的地方。我們以古典推論理論的兩個原則(動差法和概式法)為架構，檢視現有文獻的建構方式，希望此統整的角度有助辨識不同方法的特質。此外針對設限資料，我們除了討論現有文獻的做法外，並提出一個新的方法。所有的方法均透過模擬實驗檢驗其表現。

The linear transformation model, which includes the proportional hazard model and the proportional odds model, has received considerable attentions in recent years due to its flexibility. In the thesis, we consider semi-parametric estimation for the regression parameter. We review existing literature under the framework of classical inference theory. Specifically we will see how these “old” principles, namely method of moment and likelihood estimation, are applied to the modern estimation problem which involves an infinite dimensional nuisance parameter in the model formulation. After examining common techniques of handling censored data, we also propose a new approach. All the methods are evaluated by Monte Carlo simulations.