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。 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.
