跳到主要內容

簡易檢索 / 詳目顯示

回結果列表
研究生： 黃如君
Ju-chun Huang
論文名稱： 卜瓦松廣義半加法模型迴歸係數之有母數強韌推論法—探索性的研究
Robust Poisson generalized semi-additive models
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： 96
語文別： 中文
論文頁數： 63
中文關鍵詞： 廣義半母數加法模型 、強韌概似函數
外文關鍵詞： generalized semi-parametric additive models, robust likelihood function
相關次數： 點閱：7  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 本論文之目的是試著推廣Royall and Tsou (2003)所提出的強韌概似函數的概念，建立廣義半母數加法模型迴歸參數的強韌推論法，而研究之主題是以卜瓦松分配為實作模型來分析個數資料。特別強調的一點是，由於廣義半母數加法模型中有平滑函數，因此，廣義半母數加法模型並不滿足所謂的正規條件。
    文中我們推導出迴歸參數的實作概似函數的修正法，而修正過的強韌概似函數，在大樣本及二階動差存在的條件之下，提供迴歸參數的正確概似函數。模擬研究則顯示強韌概似比檢定統計量的確提供正確的統計分析。

    The purpose of this research is trying to explore the applicability of the robust likelihood methodology introduced by Royall and Tsou (2003) to the generalized semi-additive models. The focus is to develop robust likelihood inferences about regression parameters using the Poisson distribution as the working model.
    We showed details of the derivations of the adjustments that properly amends the working likelihood function. The efficacy of the proposed parametric robust method is demonstrated via simulation studies. It is shown that robust likelihood approach is effective despite the irregularity situation provoked by the nonparametric smooth function in regression.

    目錄............................................................................................................................................i 圖目錄.......................................................................................................................................ii 表目錄......................................................................................................................................iii 第一章 緒論..............................................................................................................................1 第二章 強韌廣義半母數加法模型..........................................................................................3 2-1 Robust Likelihood.....................................................................................................3 2-2 廣義半母數加法模型...............................................................................................4 第三章 卜瓦松實作模型的修正項..........................................................................................7 3-1 線性連結...................................................................................................................8 3-2 對數連結.................................................................................................................18 第四章 模擬研究....................................................................................................................27 4-1 帶寬的選取.............................................................................................................30 4-2 線性連結和對數連結的模擬結果.........................................................................31 4-3 強韌分數檢定.........................................................................................................32 第五章 結論............................................................................................................................53 參考文獻.................................................................................................................................54

    1. Casella, G. and Berger, R. L. (2002). Statistical Inference, 2nd edition. CA：Duxbury.
    2. Green, P. J. (1987). Penalized likelihood for general semi-parametric regression models.
    International Statistical Review, 55, 245-259.
    3. Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. New York：Chapman and Hall.
    4. Kalbfleisch, J.D. and Sprott, D. A. (1970). Application of likelihood methods to models involving large numbers of parameters(with discussion). JRSS-B, 32, 175-208.
    5. Opsomer, J. D. and Ruppert, D. (1999). A root-n consistent backfitting estimator for semiparametric additive modelling. Journal of Computational and Graphical Statistics, 8, 715-732.
    6. Royall, R. M. and Tsou, T-S (2003). Interpreting statistical evidence using imperfect models：Robust adjusted likelihood functions. JRSS-B, 65, 391-404.
    7. Searle, S. R. (1982). Matrix Algebra Useful for Statistics. John Wiley and Sons, New Nork,
    NY.
    8. Thurston, S. W., Wand, M. P. and Wiencke, J. K. (2000). Negative binomial additive models. Biometrics, 56, 139-144.
    9. Tsou, T-S(2005). Inferences of variance functions- a parametric robust way. Journal of Applied Statistics, 32, 785-796.
    10. Tsou, T-S(2006). Robust Poisson regression. Journal of Statistical Planning and Inference, 136, 3173-3186.
    11. Tsou, T-S(2007). A simple and exploratory way to determine the mean-variance relationship in generalized linear models. Statistics in Medicine, 26, 1623-1631.
    12. 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.
    13. Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. New York：Chapman and Hall.

    QR CODE
    :::