在模型錯誤下copula應用在迴歸分析時的正確性

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何建興(Jian-Xing He) 查詢紙本館藏

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論文名稱

在模型錯誤下copula應用在迴歸分析時的正確性
(The validity of copula for regression when model assumptions fail)

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摘要(中)

Copula 是目前分析相關性資料時，常用的一種建構聯合分配函數的一種方法，其
優點在於可以便利地建構所需的聯合分配函數，但當Copula 模型假設錯誤時，其統計
推論的正確性卻鮮有人探討。本文主要的目的是在廣義線性模型下，探討當Copula 模
型假設錯誤時，其迴歸參數之估計量是否具有一致性，且能否提供正確的統計推論，
並與Gamma-Gamma 模型、Poisson-Negative Binomial 模型以及Bivariate Negative
Binomial 模型之結果做比對。

摘要(英)

Copulas are popular and commonly used methods for constructing joint distribution
functions when analyzing correlated data. The advantage of Copulas is that one can easily
construct joint distribution functions with desired marginals. However, the validity of
inference based on Copulas under model misspecification is rarely investigated. The objective
of this paper is to examine the properties of the Copula-based estimates of the regression
parameters given that the assumptions of the Copula model fail. We also make comparisons
between several Copula models with other methods for analyzing bivariate correlated data.

關鍵字(中)

★ 相關性資料
★ 強韌概似函數
★ Copula

關鍵字(英)

★ correlated data
★ robust likelihood function
★ copula

論文目次

摘要 ....................................................................................................................................... i
Abstract ................................................................................................................................ ii
誌謝辭 ................................................................................................................................. iii
目錄 ..................................................................................................................................... iv
表目錄 ................................................................................................................................. vi
第一章緒論 ......................................................................................................................... 1
第二章 Copula ...................................................................................................................... 2
2.1 Copula 介紹 .......................................................................................................... 2
2.2 Copula 實作模型 .................................................................................................. 5
2.2.1 Copula 模型內邊際分配 ............................................................................ 6
2.2.2 Copula (Gamma, Gamma) 模型 ................................................................. 7
2.2.3 Copula (Gamma, Normal) 模型 ................................................................. 9
2.2.4 Copula (Gamma, Lognormal) 模型 .......................................................... 11
2.2.5 Copula (Gamma, Poisson) 模型 ............................................................... 13
2.2.6 Copula (Gamma, Negative Binomial) 模型 .............................................. 15
2.2.7 Copula (Bernoulli, Normal) 模型 ............................................................. 17
第三章強韌實作模型 ........................................................................................................ 20
3.1 強韌Gamma-Gamma 模型 ................................................................................ 20
3.2 強韌Poisson-Negative Binomial 模型 ............................................................... 25
3.3 強韌Bivariate Negative Binomial 模型 ............................................................. 30
第四章模擬研究 ............................................................................................................... 40
4.1 資料生成 ........................................................................................................... 40
4.2 Copula 模型相關性參數之影響 ......................................................................... 41
4.3 Gumbel Copula、Clayton Copula、Frank Copula 間之差異 .............................. 68
v
4.4 Copula 模型內邊際分配之影響 ......................................................................... 95
第五章實例分析 ............................................................................................................. 134
第六章結論 ..................................................................................................................... 137
參考文獻 ........................................................................................................................... 138

參考文獻

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139
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指導教授

鄒宗山(Tsung-Shan Tsou)

審核日期

2018-6-29

推文