博碩士論文 106225601 完整後設資料紀錄

DC 欄位 語言
DC.contributor統計研究所zh_TW
DC.creator黃昕蔚zh_TW
DC.creatorXinwei Huangen_US
dc.date.accessioned2019-7-26T07:39:07Z
dc.date.available2019-7-26T07:39:07Z
dc.date.issued2019
dc.identifier.urihttp://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=106225601
dc.contributor.department統計研究所zh_TW
DC.description國立中央大學zh_TW
DC.descriptionNational Central Universityen_US
dc.description.abstract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。zh_TW
dc.description.abstractCopula 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).en_US
DC.subject耦合zh_TW
DC.subject馬可夫鏈zh_TW
DC.subject序列相依zh_TW
DC.subject統計製程控制zh_TW
DC.subject適合度檢定zh_TW
DC.subject存活分析zh_TW
DC.subject重複觀測事件zh_TW
DC.subject相依設限zh_TW
DC.subject兩階段估計zh_TW
DC.subject摺刀法zh_TW
DC.subjectcopulasen_US
DC.subjectMarkov chainen_US
DC.subjectserial dependenceen_US
DC.subjectstatistical process controlen_US
DC.subjectgoodness-of-fiten_US
DC.subjectsurvival analysisen_US
DC.subjectrecurrent eventen_US
DC.subjectdependent censoringen_US
DC.subjecttwo-stage estimationen_US
DC.subjectjackknifeen_US
DC.titleLikelihood-based inference for copula-based Markov chain models for continuous, discrete, and survival dataen_US
dc.language.isoen_USen_US
DC.type博碩士論文zh_TW
DC.typethesisen_US
DC.publisherNational Central Universityen_US

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