半母數經驗概似函數與 有母數強韌概似函數之權衡

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姓名

蕭維政(Wei-cheng Hsiao) 查詢紙本館藏

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統計研究所

論文名稱

半母數經驗概似函數與有母數強韌概似函數之權衡
(Semi-parametric empirical likelihood versus parametric robust likelihood)

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摘要(中)

經驗概似(empirical likelihood)函數為一種不需知道母體分配的概似函數。進一步調整後的經驗概似函數能在小樣本數或估計的參數個數過多時，更快的達到大樣本近似常態性質。同樣地，Royall and Tsou (2003) 提出的有母數的強韌概似函數也提供了不需母體分配假設下完整的統計推論。
我們針對兩種概似函數做了通盤的比較，並說明上述有母數的強韌概似函數在各方面皆優於經驗概似函數。

摘要(英)

Empirical likelihood is a distribution-free approach that allows one to construct likelihood functions without knowing the true underlying distribution. Modification has been proposed to ensure that the large sample property is better achieved when sample size is not large or when there are many parameters. Alternatively, one can employ the parametric robust likelihood procedure proposed by Royall and Tsou (2003) to make likelihood inference under model misspecification.
We give a thorough comparison between the two model-independent robust likelihood approaches and show that the method by Royall and Tsou (2003) is superior to the empirical likelihood in terms of various performance benchmarks.

關鍵字(中)

★ 經驗概似函數
★ 強韌概似函數
★ 強韌概似函數

關鍵字(英)

★ Empirical likelihood
★ Robust likelihood
★ Misleading evidence

論文目次

摘要 i
Abstract ii
致謝辭 iii
Contents iv
List of Figures vi
List of Tables vii
Chapter 1 Introduction 1
Chapter 2 The adjusted EL and robust likelihood methods 4
2.1 The EL and extended AEL* 4
2.2 Statistical evidence 10
2.3 Robust likelihood function 14
Chapter 3 Robust normal and robust gamma likelihoods 17
3.1 Robust normal regression 17
3.2 Robust gamma regression 20
Chapter 4 Simulations 23
4.1 Comparisons of statistical evidence 24
4.1.1 Simulation layout for linear models 24
4.1.2 Simulation layout for log linear models 25
4.2 Comparisons of efficiency 27
4.3 Simulations with setup in Chen (1993) 30
Chapter 5 Real data analysis 55
5.1 Example 1 58
5.2 Example 2 59
Chapter 6 Concluding remarks 61
References 63

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指導教授

鄒宗山(Tsung-shan Tsou)

審核日期

2014-7-16

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