# 臺灣博碩士論文加值系統

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 本篇論文主要探討半競爭風險資料下分量迴歸的估計。由於非終端事件會受到終端事件的相關設限，使得分量迴歸的參數估計變的困難。沒有額外的假設下，我們無法對非終端事件做出推論。因此，我們利用 copula 模型說明非終端事件與終端事件之間的相關性結構。我們採用 IPW 方法估計半競爭風險下分量迴歸的參數。在 Hz(t) 已知的假設下，我們提供了此估計量的大樣本性質，並介紹模型診斷方法。根據模擬實驗的結果顯示我們所提出的方法表現的還不錯。最後，我們將應用我們所提出的方法分析骨髓移植資料作為描述。
 This thesis focuses on the quantile regression analysis for semi-competing risks data. Since the non-terminal event may be censored by the terminal event dependently, the estimation of quantile regression parameters becomes difficult. Without extra assumptions, we can not make inference on the non-terminal event. Thus, we utilize the copula function to specify the dependence between the non-terminal event time and the terminal event time. We adopt the inverse probability weight (IPW) technique to estimate the coefficients of quantile regression for semi-competing risks data. Under the assumption that Hz(t) is known, we also prove the large sample properties of the proposed estimator. We introduce a model diagnostic approach to check model adequacy. According to the simulation studies, the performance of our proposed approach are well. We also apply our approach into a real data which is Bone Marrow Transplant data for illustration.
 1 INTRODUCTION..........12 DATA and MODELS..........42.1 Semi-Competing Risks Data..........42.2 Quantile Regression Model..........52.3 Copula Model..........63 LITERATURE REVIEW..........83.1 Estimating Survival and Association in a Semicompeting Risks Model (Lakhal, Rivest and Abdous, 2008)..........83.2 Power-Transformed Linear Quantile Regression With Censored Data (Yin, Zeng and Li, 2008)..........113.3 Competing Risks Quantile Regression (Peng and Fine, 2009)..........144 THE PROPOSED INFERENCE PROCEDURE..........184.1 The Estimation of β(γ) ..........184.2 Asymptotic Properties of the Proposed Estimator..........224.3 Model Checking and Model Diagnosis..........235 SIMULATION STUDIES..........266 DATA ANALYSIS..........337 CONCLUDING REMARKS..........38References..........39Appendix..........45A Connection between Sn(b,γ) and Un(b,γ)..........45B Proofs of Theorems..........47
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 1 半競爭風險資料之餘命分量迴歸分析 2 利用插補方法分析半競爭風險資料之線性迴歸模型 3 利用插補方法分析半競爭風險資料之比例風險模型、比例勝算模型與分量迴歸模型 4 利用權重方法分析半競爭風險資料之分量迴歸 5 利用計數過程方法分析半競爭風險資料之分量迴歸 6 連續型解釋變數下半競爭風險資料之分量迴歸 7 半競爭風險資料之迴歸分析基於概似函數方法 8 半競爭風險資料下之半母數轉換模型最大概似估計 9 成對比較估計法用於半競爭風險資料之迴歸分析 10 半競爭風險資料之準獨立性檢定 11 相關設限下雙樣本存活函數之比較 12 三種資料結構下雙變數存活時間之迴歸分析

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 1 相關截切資料之迴歸分析 2 相關截切資料之分量迴歸分析 3 利用計數過程方法分析半競爭風險資料之分量迴歸 4 區域經濟中的迴歸樹模型 5 雙重截切資料與雙變數截切資料下條件 Kendall's Tau 的估計與檢定 6 貝氏空間階層模型在腸病毒資料的群聚分析 7 利用權重方法分析半競爭風險資料之分量迴歸 8 兩岸商品責任之比較研究 9 新「工會法」實施後教師組織與功能之研究 10 以分析師盈餘預測誤差的角度探討公平價值會計對企業資訊透明度之影響 11 黃金租賃利率與黃金價格之動態關聯性 12 工作拖延傾向量表初編及相關因素分析－以國軍連輔導長為例 13 利用因素分析法探究加入直銷事業的動機 14 應用因素分析與識別向量於語音情緒辨識 15 台灣跨世代華劇之暢銷關鍵因素分析

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