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研究生:楊哲奇
研究生(外文):Che-Chi Yang
論文名稱:半母數混合模型估計的一致性及其應用
論文名稱(外文):Asymptotic Consistency of the Nonparametric Maximum Likelihood Estimator in a Semiparametric Model for Cure Time and Failure Time, with Application to SARS
指導教授:張憶壽張憶壽引用關係熊昭熊昭引用關係梁賡義梁賡義引用關係劉仁沛劉仁沛引用關係趙一峰趙一峰引用關係陳玉英陳玉英引用關係劉正夫
指導教授(外文):I-Shou ChangChao A. Hsiung
學位類別:博士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:92
語文別:英文
論文頁數:40
中文關鍵詞:漸近一致性致死率無母數最大概然估計量自一致方程式嚴重急性呼吸道症候群
外文關鍵詞:severe acute respiratory syndrome(SARS)asymptotic consistencyself-consistency equationnonparametric maximum likelihood estimates(NPMLEcase fatality rate
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我們提出以半母數混合模型(Semiparametric Model)來分析死亡時間(Failure Time)和治癒時間(Cure Time)的混合資料。在這模型中我們使用無母數最大概然估計量(Nonparametric Maximum Likelihood Estimate (NPMLE))來估計死亡率(Case Fatality Rate)、回歸參數(Regression Parameter)和累積風險函數(Cumulative Hazard Function)。首先、在適當的條件下建立模型參數的Identifiability。接著證明最大概然估計量的存在性並說明其為一積分方程之解。利用此積分方程及Empirical Process Theory,證得其漸近一致性(Asymptotic Consistency)。

接著,我們利用我們所得到的積分方程和得分函數(Score Function)提出一個演算法來計算無母數最大概然估計量。使用此演算法來做統計模擬,得到了令人滿意的結果,使我們確認此模型和演算法的適切性。最後,我們使用這個模型來分析台灣疾病管制局(CDC Taiwan)所提供嚴重急性呼吸道症候群(SARS)的資料。經由我們的演算法對這些資料計算所得到的結果,對台灣嚴重急性呼吸道症候群這個傳染病建構了一個應用範圍廣泛的成果。
In this paper, we study nonparametric maximum likelihood estimators (NPMLE) in a semiparametric mixture model for cure time and failure time. This model is motivated by the study of fatality rate, time from onset to discharge and time from onset to death for SARS (severe acute respiratory syndrome) patients. SARS patients are kept in isolation until recovery or death.
Because of no known treatment or preventive measure, it is important to know the case fatality rate and
the distribution of admission-to-death and admission-to-discharge for the study of transmission dynamics
and for better planning of patient care capacity. The identifiability of the parameters, the existence of NPMLE, and their asymptotical consistency are established under certain regularity conditions. We also propose a self-consistency based algorithm for computing the nonparametric maximum likelihood estimates
in this model.
The performance of this method is successfully demonstrated in a simulation study and in the analysis of Taiwan SARS data.
1. Introduction 1
2. Nonparametric Maximum Likelihood Estimate 5
3. Asymptotic Consistency of NPMLE 13
4. An Algorithm 21
5. A Simulation Study 23
6. Application to Taiwan SARS Data 24
7. Concluding Remarks 25
Appendix 30
References 37
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