增长曲线模型中回归系数的广义岭型主成分估计

The combining generalized ridge and principal components estimator of regression coefficient in growth curve model

针对增长曲线模型中设计阵呈病态时,提出了一种有偏估计——广义岭型主成分估计:证明了通过选择适当的参数,使得该估计在均方误差(MSE)意义下改善了最小二乘估计和主成分估计,并且进一步得到了在MSE意义下该估计是可容许估计,最后得到该估计在广义岭型降维估计类中方差和最小。

A new estimator of regression coefficients called the combining generalized ridge and principal components estimator is proposed to solve the problem that the design matrices of growth curve model are likely to be illconditioned. It was proved that under the MSE principal this estimator was superior to least squares estimator and principal components estimator with an appropriate selection of parameters. The. admissibility was also proved under the MSE principal. Furthermore, it was proved that the combining generalized ridge and principal components estimator had the minimum variance sum in the class of generalized ridge reduced dimension estimator.