如果數據包含異常值與多重共線性時，則通常相較於最小平⽅法會選用 Ridge M-estimator(Silvapulle 1991)。因為當數據同時具有異常值與多重共線性的情況下，Ridge M-estimator 會有較小的MSE。許多的估計量，例如：Pretest M-estimators, Stein-type shrinkage M-estimators，都類似Ridge M-estimator。然⽽現在所有的ridge estimators 和M-estimators 都沒有考慮截距項的收縮估計。因此存在改進現有估計量的空間，可透過改進截距項的估計⽽達成。在本⽂中，我們透過引⼊截距項的估計⽅法，在線性模型中引⼊新的 robust estimators 的估計。為了說明，我們分析了從數據提取系統（KGUSBADES）提供的Nikkei NEEDS 公司財務數據。本論⽂是與Kwansei Gakuin ⼤學的Jimichi Masayuki 博⼠及其同事合作的⼀部分。但是，所有統計分析都是由作者進⾏的。;If the data contains outliers and multicollinearity, the ridge M-estimator (Silvapulle 1991) is the preferred estimator to the usual least square estimator. In fact, the ridge M-estimator has the smaller mean square error in the presence of outliners and multicollinearity. Many other estimators, such as the pretest M-estimators and Stein-type shrinkage M-estimators follow similar approaches to the ridge M-estimator. However, all the existing ridge and M-estimators do not consider shrinkage estimation for the intercept term. Hence, there is a room for improving the existing estimators by improving the estimator of the intercept. In this thesis, we introduce new robust estimators of regression coefficients in a linear model by introducing a pretest estimation method for an intercept. For illustration, we analyze the Nikkei NEEDS corporate finance data that are provided from the data-extraction system (KGUSBADES). This thesis is part of collaboration with Dr. Jimichi Masayuki and his olleagues in Kwansei Gakuin University. However, all the statistical analyses are conducted by the author.
