Likelihood-based inference for copula-based Markov chain models for continuous, discrete, and survival data

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黃昕蔚(Xinwei Huang) 查詢紙本館藏

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統計研究所

論文名稱

(Likelihood-based inference for copula-based Markov chain models for continuous, discrete, and survival data)

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摘要(中)

利用耦合對序列相依關係建模在過往文獻中已被廣泛地探討了。然而，鮮少針對基於耦合的馬可夫鏈模型進行診斷的討論。此外，由於複雜的設限機制，基於耦合的馬可夫鏈模型對序列相依的存活數據建模也是一個難題。本文在連續型數據、離散型數據和存活數據，此三種數據形態下，以概似函數為基礎對基於耦合的馬可夫鏈模型進行擬合。對連續型和離散型數據，我們提出適合度檢定以及利用概似函數選擇模型的模型診斷策略。而針對存活數據，我們則建構了一個全新的基於耦合的馬可夫鏈模型，用於對序列相依的重複觀測事件進行建模。模型中的相依設限也被耦合所考慮。兩種耦合的存在使概似函數極為複雜，故此，我們採用兩階段估計方法。基於估計函數理論，漸近變異數可以被理論證明。對此，我們提出摺刀法作為漸近變異數的一致估計量，從而進行區間估計。對三種類型數據的生成與建模，我們都提供了便於使用的R語言函數。所有提出的方法都經過了模擬驗證，並且利用五筆真實數據（化學數據、財務數據、棒球數據、股市數據和存活數據）進行分析與說明。

摘要(英)

Copula modeling for serial dependence has been extensively discussed in the literature. However, model diagnostic methods in copula-based Markov chain models are rarely discussed in the literature. Also, copula-based Markov modeling for serially dependent survival data is challenging due to the complex censoring mechanisms. The thesis studies likelihood-based model fitting methods under copula-based Markov chain models on three types of data structures, continuous, discrete and survival data. For continuous and discrete data, we propose model diagnostic procedures, including a goodness-of-fit test and a likelihood-based model selection method. For survival data, we propose a novel copula-based Markov chain model for modeling serial dependence in recurrent event times. We also use a copula for modeling dependent censoring. Due to the complex likelihood function with the two copulas, we adopt a two-stage estimation method for fitting the survival data, whose asymptotic variance is derived by the theory of estimating functions. We propose a jackknife method for interval estimates, which is shown to be consistent for the asymptotic variance. We develop user-friendly R functions for simulating the data and fitting the models for continuous, discrete, and survival data. We conduct simulation studies to see the performance of all the proposed methods. For illustration, we analyze five datasets (chemical data, financial data, baseball data, stock market data, and survival data).

關鍵字(中)

★ 耦合
★ 馬可夫鏈
★ 序列相依
★ 統計製程控制
★ 適合度檢定
★ 存活分析
★ 重複觀測事件
★ 相依設限
★ 兩階段估計
★ 摺刀法

關鍵字(英)

★ copulas
★ Markov chain
★ serial dependence
★ statistical process control
★ goodness-of-fit
★ survival analysis
★ recurrent event
★ dependent censoring
★ two-stage estimation
★ jackknife

論文目次

Chapter 1 Introduction 1
Chapter 2 Copula models 3
2.1 Copulas 3
2.2 Copula-based Markov chain 6
2.3 Discrete margins 8
2.4 Survival copula 9
Chapter 3 Continuous data 11
3.1 Continuous data in SPC 11
3.2 Copula-based Markov chain model 12
3.3 Likelihood 13
3.4 Asymptotic properties 15
3.5 Goodness-of-fit 17
3.6 Model selection 19
3.7 Software 20
3.8 Data analysis 22
Chapter 4 Attribute data 29
4.1 Attribute data in SPC 29
4.2 Copula-based Markov chain model 30
4.3 Maximum likelihood estimation 31
4.4 Asymptotic properties 33
4.5 Goodness-of-fit 34
4.6 Model selection 36
4.7 Software 37
4.8 Data analysis 39
Chapter 5 Survival data 42
5.1 Recurrent event data 42
5.2 Model and likelihood 45
5.3 Clayton copula and Weibull model 47
5.4 Two-Stage maximum likelihood method 48
5.5 Asymptotic properties 49
5.6 Computation 51
5.7 Simulation 51
5.8 Software 57
5.9 Data analysis 59
Chapter 6 Conclusion 65
Appendix A 68
Appendix B 69
Appendix C 77
References 85

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指導教授

江村剛志(Takeshi Emura)

審核日期

2019-7-26

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