相關性資料的有母數強韌推論

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陳建宏(Chien-Hung Chen) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

相關性資料的有母數強韌推論
(Parametric Robust Inferences for Correlated Data)

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摘要(中)

本論文中，先介紹由 Royall 與 Tsou 在2003年所提出的強韌概似函數的觀念。利用這個方法，首先建立了對於二變數資料的相關係數在廣義線性模型架構下的迴歸參數的強韌概似比檢定。其次，對於具有相關性的個數資料的平均數，建立一個強韌分數檢定。最後，對於上述具有相關性的個數資料的平均數在廣義線性模型架構下，對於迴歸參數建立一個強韌概似比檢定。
這些概似函數並不需要知道資料的真正分配，只要四階或二階動差存在即可。這些強韌方法的效率，經由模擬與真實資料呈現。

摘要(英)

In this thesis, we introduce the robust likelihood function proposed by Royall and Tsou (2003). Based on the method we first establish a robust parametric likelihood ratio test about regression parameters for the correlation coefficients modeled in a generalized linear model fashion. Next, we construct a robust parametric score test to compare means of several dependent populations of count. Furthermore, a robust parametric likelihood ratio test for regression parameters of means for correlated count data is proposed.
The validity of the proposed likelihoods requires no knowledge of the true underlying distributions, so long as they have finite fourth or second moments. The efficacy of the robust methodology is demonstrated via simulations and real examples.

關鍵字(中)

★ 二維常態
★ 強韌概似比檢定
★ 多變數負二項模型
★ 廣義線性模型
★ 強韌分數檢定

關鍵字(英)

★ Multivariate negative binomial
★ Bivariate normal

論文目次

Abstract ii
Acknowledgements iii
Contents iv
List of Tables v
1 Introduction 1
2 Robust Inferences Based on the Adjust Likelihood and GEE 3
2.1 Model Misspecification 3
2.2 Robust Adjusted Likelihood Functions 4
2.3 The GEE Method 7
3 Parametric Robust Inference about Regression Parameters for Correlation Coefficient 9
3.1 Introduction 9
3.2. Making the Bivariate Normal Likelihood Robust 10
3.3 Simulation Studies 16
3.4 Discussion 19
4 Comparing Means of Several Dependent Populations of Count 21
4.1. Introduction 21
4.2 The Multivariate Poisson Model 22
4.3 Making the Multivariate Negative Binomial Likelihood Robust 24
4.4 Simulation Studies 30
4.5. A Real Example 33
4.6. Discussion 36
5 Robust Regressions of Means for Correlated Count Data 37
5.1 Introduction 37
5.2 The Robust Likelihood 38
5.3 Simulation Studies 43
5.4 An Example 46
5.5 Discussion 49
References 50
Appendix A 53
Appendix B 59
Appendix C 71

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指導教授

鄒宗山(Tsung-Shan Tsou)

審核日期

2007-7-12

推文