摘要 Tsou (2004)將Royall and Tsou (2003)提出之強韌概似函數的方法推廣到在廣義線性模型之下迴歸係數推論上，進而提出了概似函數的修正法。而修正過的概似函數，在大樣本時，只要觀察值的真正分配有二階動差，便可對迴歸係數提供正確的推論。Tsou (2003)則是利用同樣強韌概似函數的方法提出了具有強韌性的有母數檢定法來比較分配未知的母體變異數。 本研究將把上述的強韌法推廣到連結函數的強韌推論上。將常態、伽瑪和逆高斯實作模型進行修正，得到在大樣本時及一些正規條件下正確的連結函數的概似函數。並利用修正後的強韌概似比檢定、分數檢定以及Wald檢定來顯示此強韌性。另外，也對常被用分析個數資料的卜瓦松迴歸模型進行修正。 Abstract Tsou (2004) extends the robust likelihood functions that was proposed by Royall and Tsou (2003) to the reference of the regressive coefficients in general linear model, and proposes the adjust method of likelihood functions. In large sample, if true distribution of observations just has the second moment, the likelihood functions that have been adjusted will provide the correct reference for regressive coefficients. Tsou (2003) applied the similar method that proposed the testing method of robust parametric to compare the population variance of unknown distribution. In this paper, we apply the robust method of the above to the robust reference of link functions. According to the adjusted working model of normal, gamma and inverse gauss, we get the likelihood functions of the correct link functions in large sample and in some regular conditions. We show that it is robust by the adjusted robust likelihood test, score test and Wald test. Furthermore, we adjust the Poisson working model that are often used to analyse the count data.
