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研究生： 游菀菁
Wan-Jing You
論文名稱： 二元資料之連結函數之有母數強韌迴歸
指導教授： 鄒宗山
Tsung-Shan Tsou
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 94
語文別： 中文
論文頁數： 48
中文關鍵詞： 二元資料
外文關鍵詞： binary data
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    • 摘要
    二元資料之分析大部分的情形都是使用邏輯斯迴歸模型。但事實上，適合之模型不見得是邏輯斯迴歸模型。
    本文之目的在使用Royall and Tsou(2003)之強韌概似函數法。將二項分配模型做適當之修正後，使得在大樣本之情形下，即使二元資料之分配非二項分配，亦能對連結函數做正確之推論。

    Abstract
    This thesis utilizes the robust likelihood technique proposed by Royall and Tsou(2003) to develop parametric robust inferences about the link function for binary response variables.
    More specifically, the binomial model is corrected to become robust. With large samples the adjusted binomial likelihood is asymptotically legitimate for the relationship of interest. One needs not know whether the binary data are correlated or not, or the extent of the correlation exists in data. Simulations are used to demonstrate the efficacy of the proposed robust method.

    目錄 第一章 緒論 ………………………………………………………1 第二章 強韌迴歸 …………………………………………………3 第三章 修正項 ……………………………………………………6 3.1 二項實作模型之下連結函數的修正項 ………………………6 3.2 邏輯斯迴歸模型下，迴歸係數的修正項 ……………………21 第四章 簡單迴歸…………………………………………………33 第五章 模擬研究…………………………………………………35 5.1.1 強韌二項迴歸 ……………………………………………35 5.1.2 強韌二項迴歸模擬研究 …………………………………36 5.1.3 強韌二項迴歸模擬結果 …………………………………37 5.2.1 邏輯斯迴歸模型下的強韌二項迴歸 ……………………38 5.2.2 邏輯斯迴歸模型下的強韌二項迴歸模擬研究 …………38 5.2.3 邏輯斯迴歸模型下的強韌二項迴歸模擬結果 …………39 第六章 結論………………………………………………………42 參考文獻 ………………………………………………………………43

    參考文獻
    1. Francisco J. Aranda-Ordaz (1981). On two families of transformations to additivity for binary response data. Biometrika, 68, 2, 357-363.
    2. Royall, R.M., and Tsou, T-S (2003). Interpreting statistical evidence using
    imperfect models: Robust adjusted likelihood functions. Journal of the Royal
    Statistical Society. Series B (Statistical Methodology), 65, 391-404.
    3. Tsou, T-S (2003). Comparing two population means and variances - a parametric
    robust way. Communications in Statistics - Theory and Methods, 32, 10,
    2013-2019.
    4. Tsou, T-S and K-F Cheng (2004) Parametric robust regression analysis of
    contaminated data. Communications in Statistics - Theory and Methods, 33,
    1887-1898.
    5. Tsou, T-S and Chien, L-C (2005). Parametric robust tests for multiple regression parameters under generalized linear models. Advances and Applications in Statistics, 1, 51-86.
    6. Tsou, T-S (2005a). Robust inferences for the correlation coefficient – a parametric robust way. Communications in Statistics - Theory and Methods, 34, 147-162.
    7. Tsou, T-S (2005b). Inferences of variance functions- a parametric robust way.
    Journal of Applied Statistics, Vol. 32:785-796.
    8. Tsou, T-S (2006a). Robust Possion regression. Journal of Statistical Planning and Inference, 136, 3173-3186.
    9. Tsou, T-S (2006b). A simple and exploratory way to determine the mean-variance relationship in generalized linear models. (to appear in Statistics in Medicine)

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