成對/配對二分資料的強韌概似分析

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姓名

林宇涵(Yu-Han Lin) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

成對/配對二分資料的強韌概似分析
(Robust likelihood analysis of paired/matched binary data)

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摘要(中)

成對/配對設計引入了相關性/聯合機率，因而使分配間的比較更複雜。本文提出一個強韌概似函數方法來推論配對設計下三個伯努利分配的異同。此強韌法是將三個獨立的伯努利概似函數強韌化，得到強韌分數統計量來檢定三個伯努利分配是否相同。我們並進一步的在模型內加入自變量以考慮配對設計的情境。
本文中提出了理論證明與推導，並利用模擬和實例分析來展示強韌化方法的正確性，以及與非強韌化方法做比較所展示的優勢。

摘要(英)

Paired/matched designs introduce correlation/joint probabilities to the probability structure that complicates the analysis considerably. In the thesis, we propose a robust likelihood function approach to inference about the difference between three Bernoulli distributions in paired/matched situations. The robust likelihood is constructed by amending the independent working model. One could acquire a robust score test statistic for testing the homogeneity of three binary populations without modeling correlation/joint probabilities. We further incorporate covariates in the matched scenario. We use simulations and real data analysis to demonstrate the merit of out robust likelihood methodology.

關鍵字(中)

★ 相關性二元資料
★ 成對設計
★ 強韌概似函數
★ 強韌分數檢定

關鍵字(英)

★ Correlated binary data
★ paired designs
★ robust likelihood function
★ robust score test

論文目次

目錄
摘要 ............................................................................................................................................ i
Abstract ...................................................................................................................................... ii
誌謝辭 ...................................................................................................................................... iii
目錄 .......................................................................................................................................... iv
表目錄 ...................................................................................................................................... vi
第一章緒論 .............................................................................................................................. 1
第二章三個伯努利模型之強韌化：模型Ⅰ .......................................................................... 4
2.1 最大概似估計量.............................................................................................................. 5
2.2 實作模型之費雪訊息矩陣.............................................................................................. 6
2.3 分數函數的變異數矩陣 .................................................................................................. 9
2.4 1 與 2之非強韌分數統計量...................................................................................... 16
2.5 1 2  與  之強韌分數統計量.......................................................................................... 20
第三章具自變量之強韌伯努利模型：模型Ⅱ .................................................................... 23
3.1 最大概似估計量............................................................................................................ 24
3.2 實作模型之費雪訊息矩陣 ............................................................................................ 25
3.3 分數函數的變異數矩陣................................................................................................ 30
3.4 1 2  與  之強韌分數統計量.......................................................................................... 42
v
3.5 自變量為二元資料........................................................................................................ 43
3.5.1 實作模型之費雪訊息矩陣 ......................................................................................... 43
3.5.2 分數函數的變異數矩陣 ......................................................................................... 45
3.5.3 1
 與2
 之強韌分數統計量 .................................................................................... 51
第四章模擬研究 .................................................................................................................... 53
4.1 模型Ⅰ：資料生成方式................................................................................................ 53
4.2 模型Ⅱ：資料生成方式................................................................................................ 55
4.3 模擬結果........................................................................................................................ 56
第五章實例分析 .................................................................................................................... 86
第六章結論 ............................................................................................................................ 95
參考文獻 ................................................................................................................................. 96

參考文獻

Kenneth, S. M. (1981). On the inverse of the Sum of Matrices. Mathematics Magazine,
54:67-72.
Liu, J. P., Hsueh, H. M., Hsueh, E. and Chen J. J. (2002). Tests for equivalence or
non-inferiority for paired binary data. Statistics in Medicine, 21:231-245.
Miyashita, N., Kawai, Y., Yamaguchi, T. and Ouchi, K. (2011). Clinical potential of
diagnostic methods for the rapid diagnosis of Mycoplasma pneumoniae pneumonia in
adults. Eur J Clin Microbiol Infect Dis, 30:439-446.
Qaqish, F. B. (2003). A family of multivariate binary distributions for simulating correlated
binary variables with specified marginal means and correlations. Biometrika,
90:455-463.
Ron, J. and Michael, G. K. (1987). Modelling binary data from a three-period cross-over trial.
Statistics in Medicine, 6:555-564.
Royall, R. M. and Tsou, T. S. (2003). Interpreting statistical evidence by using imperfect
models: robust adjusted likelihood functions. Journal of the Royal Statistical Society,
Series B, 65:391-404.
Tsou, T. S. and Chen, C. H. (2008). Comparing several means of dependent populations of
count-A parametric robust approach. Statistics in Medicine, 27:2576-2585.
97
Tsou, T. S. (2017). A robust likelihood approach to inference about the difference between
two multinomial distributions in paired designs. Statistical Methods in Medical Research,
0:1-15.

指導教授

鄒宗山(Tsung-Shan Tsou)

審核日期

2018-6-29

推文