具異質性多變量線性模型之廣義推論

Abstract

本論文主題在利用廣義方法處理具異質性AR(1)共變異矩陣之迴歸模型，由Tsui 與 Weerahandi (1989) 和 Weerahandi (1993) 提出廣義p值和廣義信賴區間的觀念提供不同於傳統處理異質性方法，我們把廣義p值和廣義信賴區間推廣到廣義多變量檢定統計量的標準化。Lin and Lee (2003)應用廣義p值和廣義信賴區間處理具異質性uniform共變異矩陣之多變量變異數分析問題，我們利用他們的程序並做適度修改來處理具異質性AR(1)共變異矩陣之迴歸模型，所得到的涵蓋機率與預期面積是令人滿意的結果。同時我們的方法也適用於uniform共變異矩陣且無需限定design matrices 具特定形式。

Our main subject in this dissertation is applying the generalized method to deal with regression model with heteroscedastic AR(1) covariance matrices. The concepts of the generalized p-values and the generalized confidence intervals proposed by Tsui and Weerahandi (1989) and Weerahandi (1993), respectively, provide an alternative way to handle with heteroscedasticity. We extend these concepts to further consider the standardized expression of the generalized multivariate test variable. Lin and Lee (2003) applied the generalized method to deal with the MANOVA model with unequal uniform covariance structures among multiple groups. We utilize their process with modifications to deal with regression model with heteroscedastic serial dependence. The coverage probabilities and expected areas based on our proposed procedure display satisfactory results. Besides, we also find that our method can be applied to the uniform structures without the special design matrices assumption.