复共线性与广义岭型估计

Approximate Multicollinearity and Generalized Ridge Estimation

针对线性回归模型Y=Xβ+l的典则形式Y=a01+Z+l,l^(0,σ2I)在设计阵X呈病态时,提出了一类新估计■(k;q)=〔Λ1OOkIq+Λ2〕-1Z′Y,称之为广义岭型估计.优点是结合主成分估计和岭估计的思想和方法,将X′X的特征值分为不同大小属性的两部分Λ1与Λ2,并分别添加不同的常数,致使新估计类的均方误差大幅降低的同时计算量大大减少,而且便于对原变量做出解释.文中进一步讨论了该估计优于岭估计的k的存在性以及充分条件.

Considering the linear regression model, Y=a01＋Z ＋l,l-（0,σ^2I）, in terms of the approximate multicollinearity of the original data matrix, this paper gains the generalized ridge estimation of the parameter , named （k;q）, with the ideas and methods of the principal components and the ridge estimation, its advantage is lower calculation and is easy to explain the model. Then it further discusses the sufficient condition of （k superior to （k） .