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研究生： 沈仲維
Chung-Wei Shen
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
指導教授： 鄒宗山
Tsung-Shan Tsou
口試委員:
學位類別： 博士
Doctor
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 97
語文別： 英文
論文頁數： 64
中文關鍵詞： 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
外文關鍵詞： Partially linear models, Generalized Linear models, Robust likelihood function, Correlated ordinal data
相關次數： 點閱：13  下載：0 
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    • 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。

    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.

    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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