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姓名 賴佳民(Jia-min Lai) 查詢紙本館藏 畢業系所 統計研究所 論文名稱 負二項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 相關論文 檔案 [Endnote RIS 格式] [Bibtex 格式] [相關文章] [文章引用] [完整記錄] [館藏目錄] [檢視] [下載]
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摘要(中) 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,而研究之主題是以負二項分配為實作模型來分析個數資料。特別強調的一點是,由於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。摘要(英) 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 negative binomial 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.關鍵字(中) ★ 強韌概似函數
★ 廣義半母數加法模型
★ 負二項關鍵字(英) ★ negative binomial
★ generalized additive model
★ robust likelihood論文目次 第一章 緒論................................................... 1
第二章 強韌廣義半母數加法模型................................. 2
第三章 修正項................................................. 5
3.1 線性連結............................................... 5
3.2 對數連結.............................................. 24
第四章 模擬研究.............................................. 43
4.1 r 的選取............................................... 47
4.2 模擬在線性連結和對數連結的情況........................ 61
第五章 結論.................................................. 74
參考文獻..................................................... 75參考文獻 [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 Satistical 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 York, 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 and Chen, C-H (2008). Comparing several means of dependent populations of count-a parametric robust approach. Statistics in Medicine, 27, 2576-2585.指導教授 鄒宗山(Tsung-shan Tsou) 審核日期 2008-6-19 推文 facebook plurk twitter funp google live udn HD myshare reddit netvibes friend youpush delicious baidu 網路書籤 Google bookmarks del.icio.us hemidemi myshare