广义岭型压缩主分量估计及其优良性

Generalized Ridge-Type Shrunken Principal Components Estimator and Its Optimality

对线性回归模型回归系数β,当设计阵X为病态时,提出一种新估计:广义岭型压缩主分量估计,它在MSE和GMSE准则下优于最小二乘估计,在均方误差准则下优于岭型压缩主成分估计,最后对它的可容许性进行了讨论。

A new,generalized ridge-type shrunken principal components estimator,is proposed for the regression coefficients of a linear regression model when the design matrix X is ill-conditioned.The result shows that it is better than LSE under MSE and GMSE criterion and better than ridge-type shrunken principal components estimator under MSE criterion.Finally,its admissibility is discussed.