### 博碩士論文 93245002 詳細資訊

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(Composite estimating equations for correlated data)

 ★ 不需常態假設與不受離群值影響的選擇迴歸模型的方法 ★ 用卜瓦松與負二項分配建構非負連續隨機變數平均數之概似函數 ★ 強韌變異數分析 ★ 用強韌概似函數分析具相關性之二分法資料 ★ 利用Bartlett第二等式來估計有序資料的相關性 ★ 相關性連續與個數資料之強韌概似分析 ★ 不偏估計函數之有效性比較 ★ (一)加權概似函數之強韌性探討 (二)影響代謝症候群短期發生及消失的相關危險因子探討 ★ 利用 Bartlett 第二等式來推論模型假設錯誤下的變異數函數 ★ (一)零過多的個數資料之變異數函數的強韌推論 (二)影響糖尿病、高血壓短期發生的相關危險因子探討 ★ 一個分析具相關性的連續與比例資料的簡單且強韌的方法 ★ 時間數列模型之統計推論 ★ 複合概似函數有效性之探討 ★ 決定分析相關性資料時統計檢定力與樣本數的普世強韌法 ★ 檢定DNA鹼基替換模型的新方法 - 考慮不同DNA鹼基間的相關性 ★ 針對名目、個數與有序資料迴歸係數統計檢定力計算的普世強韌法

This thesis proposes a semi-parametric means of analyzing correlated or independent data whose underlying distributions need not to be known. The idea is to combine two estimating equations, one for independent data and one to accommodate the nature of within-cluster association existing in data. The proposed method is named the composite estimating equations.
The performance of the composite estimating equations will be investigated in terms of their asymptotic properties, such as the asymptotic normality and the efficiency. The aim of this study is to establish the most efficient estimate of the regression parameter of interest in the composite estimating equations under the generalized linear model. Optimal formulas have been shown in generalized simple linear regression models without intercepts, and in simple linear regression model with intercepts. An analytical expression of the optimal estimate does not exist in generalized multiple regression models. Hence, we adopt the approximation method to deal with problem of optimality.
A simulation is carried out to provide a comparison between various composite estimating equations as well as composite estimating equations with generalized estimating equations (Liang and Zeger, 1986) and composite likelihood (Lindsay, 1988) that are usual used for correlated data. Several examples are used to demonstrate the efficacy of the proposed method.

★ 群組資料
★ 廣義估計方程式
★ 複合估計方程式
★ 複合概似函數
★ 多元負二項
★ 相關性資料

★ Composite estimating equations
★ Composite likelihood
★ Clustered data
★ Longitudinal data
★ Correlated data
★ Multivariate negative binomial

1 Introduction 1
2 Composite estimating equations 5
2.1 Composite estimating equations . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Unbiasedness of CEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Generalized estimating equations . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Composite likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Sandwich variance 13
4 Efficient estimate 15
4.1 Generalized simple linear regression without intercepts for simple versions of CEE 15
4.2 Simple linear regression with intercepts for a simple version of CEE related to
the independent normal score . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Administration of optimal problem . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 Simulations 34
5.1 Comparison within the optimal formulas of CEE for p = 1 and p = 2 . . . . . . 35
5.1.1 Independent normal data for p = 1 . . . . . . . . . . . . . . . . . . . . . 35
5.1.2 Dependent data for p = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.1.3 Independent normal and dependent data for p = 2 . . . . . . . . . . . . . 37
5.2 Comparison within various versions of CEE for p = 3 . . . . . . . . . . . . . . . 37
5.2.1 Independent normal data for p = 3 . . . . . . . . . . . . . . . . . . . . . 38
5.2.2 Dependent normal data for p = 3 . . . . . . . . . . . . . . . . . . . . . 38
5.3 Compare CEE with GEE and CL . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3.1 Independent data for p = 3 . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3.2 Dependent data for p = 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 42
i
6 Real examples 43
7 Conclusions and future work 47
References 49
Appendix A 51
Appendix B: Tables 53
List of Figures
1 Comparison of B=(mA2)) with it three components . . . . . . . . . . . . . . . . 18
2 Sandwich estimate of (2) under various φ values . . . . . . . . . . . . . . . . . . 31
3 Sandwich estimate of (1) under various φ values . . . . . . . . . . . . . . . . . . 31
4 Sandwich estimate of (8) under various φ values . . . . . . . . . . . . . . . . . . 32
5 Sandwich estimate of (12) under various φ values . . . . . . . . . . . . . . . . . 32
List of Tables
1 Results for the mouth rinse data . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2 Results for the hospital visit data . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 Results for the small mice data . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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