本論文之目的是試著利用Royall and Tsou (2003) 所提出的強韌概似函數 的概念,將其推廣到廣義部分線性模型的架構下且資料是具有相關性時,如 何對有興趣的迴歸參數做推論。而研究之主題分別以常態分配及二項分配為 實作模型來分析有相關性之連續型資料和二元資料。特別強調的一點是,由 於廣義部分線性模型中有平滑函數,因此,廣義部分線性模型並不滿足所謂 的正規條件。在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分數檢定統計量可以提供正確的統計分 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 partial linear models. We adopt the Normal and Binomial distribution as the working model when the data is dependent to develop robust likelihood function for the regression parameters in GPLM. 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 even in irregularity situations caused by the components of the smooth function.