強韌概似函數更廣泛之應用

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沈仲維(Chung-Wei Shen) 查詢紙本館藏

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統計研究所

論文名稱

強韌概似函數更廣泛之應用
(More on the Applicability of the Robust Likelihood Methodology)

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摘要(中)

本論文首先介紹Royall與Tsou在2003年所提出之強韌概似函數的方法。其次，將其方法與觀念，應用於分析相關性的有序(ordinal)資料並於資料平均數在廣義線性模型的架構下，推導大樣本時，有興趣之迴歸參數的強韌概似函數。最後，將平均數由廣義線性模型進ㄧ步推廣到部分線性模型的架構且同樣推導大樣本時，有興趣之迴歸參數的強韌概似函數。
值得注意的是這些概似函數並不需要知道資料的真實分配，只需要假設二階或四階動差存在即可。最後，利用模擬與真實資料的分析來呈現此強韌方法的效率。

摘要(英)

In this thesis, we first introduce the idea of robust likelihood functions proposed by Royall and Tsou (2003). Next, we provide a parametric robust method originated from this idea to make inferences for correlated ordinal data and develop the robust likelihood functions for regression coefficients of mean modeled in a generalized linear model fashion. Finally, we extend the robust likelihood technique from generalized linear models (GLM) to partially-linear models (PLM), and use normal distribution as the working model to develop the robust likelihood functions for regression coefficients in large samples.
The legitimacy of this novel approach requires no knowledge of the underlying joint distributions so long as their second or fourth moments exist. The efficacy of the proposed parametric approach is demonstrated via simulations and the analyses of several real data sets.

關鍵字(中)

★ 部份線性模型
★ 廣義線性模型
★ 強韌概似函數
★ 相關性的有序資料

關鍵字(英)

★ Partially linear models
★ Generalized Linear models
★ Robust likelihood function
★ Correlated ordinal data

論文目次

Abstract ii
Contents iv
List of Tables vi
1 Introduction 1
2 Robust Inferences Based on Adjust Likelihood Methodology3
2.1 Model Misspecification 3
2.2 Robust Adjusted Likelihood Functions 5
3 Parametric Robust Inferences for Correlated Ordinal Data
10
3.1 Introduction 10
3.2 The Multinomial Model 12
3.3 Making the Multinomial Likelihood Function Robust 14
3.4 Implementation 14
3.5 Simulation Studies 16
3.6 Real Examples 18
3.7 Concluding Remarks 20
4 Robust Likelihood Inference for Regression Parameters in
Partially–linear Models 22
4.1 Introduction 22
4.2 Partially linear models (PLM) 23
4.3 Making the Normal Likelihood Function Robust 25
4.3.1 Calculating the Adjusted Robust Penalized
Likelihood 26
4.3.2 Bandwidth Choice.31
4.4 Simulation Studies.32
4.5 Illustrative Examples.39
4.6 Conclusions 43
References 44
Appendix A 47
Appendix B 48
Appendix C 52
Appendix D 54
Appendix E 56
Appendix F 62

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指導教授

鄒宗山(Tsung-Shan Tsou)

審核日期

2009-6-10

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