Likelihood inference on bivariate competing risks models under the Pareto distribution

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姓名

李威(Wei Lee) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Likelihood inference on bivariate competing risks models under the Pareto distribution)

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摘要(中)

本篇論文研究在二元柏拉圖分配下競爭風險(competing risks)資料的概似推論。第一個模型是邊際分配為柏拉圖分配的富蘭克聯結函數(Frank copula)，第二個模型是由Sankaran以及Nair(1993)提出的二元柏拉圖分配(SNBP)。我們會介紹上述分配的資料生成演算法，推導出score function以及Hessian matrix的形式，並使用牛頓-拉弗森演算法(Newton-Raphson algorithm)來找出概似函數的最大值。我們利用圖形比較和信息標準來發展適合度檢定，我們設計了模擬研究來檢視我們的最大概似估計量，並檢查所有方法的正確性，最後使用一組真實資料來做分析。

摘要(英)

This thesis studies likelihood inference based on competing risks data under bivariate Pareto models. The first model is the Frank copula model with the Pareto marginal distributions. The second one is the Sankaran and Nair bivariate Pareto (SNBP) model, which is a bivariate Pareto distribution introduced by Sankaran and Nair (1993). We introduce data-generating algorithms from these distributions. We derive the forms of the score and Hessian matrix and develop a Newton-Raphson algorithm for maximizing the likelihood function. We develop goodness-of-fit methods by graphical plots and information criteria. We execute simulation study to examine the performance of the maximum likelihood estimators, checking the correctness of all our methods. Last we analyze a real dataset for illustration.

關鍵字(中)

★ 競爭風險
★ 富蘭克聯結函數
★ 二元柏拉圖分配
★ 肯德爾相關係數
★ 牛頓-拉弗森

關鍵字(英)

★ Competing risks
★ Frank copula
★ Bivariate Pareto distribution
★ Kendall′s tau
★ Newton-Raphson

論文目次

Chapter 1 Introduction………………………………………………………………1
Chapter 2 Bivariate Pareto model……………………………………3
2.1 Pareto distribution (one dimensional)…………………………3
2.2 Copula function……………………………………………………4
2.3 The bivariate Pareto model with the Frank copula…………5
2.4 The SNBP distribution and the LSBP distribution…………6
Chapter 3 Competing risks analysis under the Frank copula model………………………………………………………………………7
3.1 Maximum likelihood inference under common margins………7
3.2 Maximum likelihood inference under different margins…12
3.3 Simulation…………………………………………………………16
Chapter 4 Competing risks analysis under the SNBP model……18
4.1 Maximum likelihood inference…………………………………18
4.2 Simulation…………………………………………………………22
Chapter 5 Goodness-of-fit……………………………………………24
Chapter 6 Simulation…………………………………………………27
Chapter 7 Data analysis………………………………………………42
Chapter 8 Conclusion…………………………………………………49
Appendix 1………………………………………………………………51
Appendix 2………………………………………………………………57
Appendix 3………………………………………………………………64
References………………………………………………………………65

參考文獻

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指導教授

江村剛志

審核日期

2017-6-27

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