线性模型的广义岭型组合主成分估计

Combining generalized ridge principal component estimate in linear model

对设计阵X呈病态的线性回归模型,提出回归系数有偏估计的一种广义岭型主成分估计.均方误差意义下,在一定条件下它优于岭型主成分估计、Stein型主成分估计.证明了它的可容许性和较强的抗干扰性以及Pit-man准则下的优良性.

In this article, a new biased estimate to the coefficient of regression：Combining Generalized Ridge Principal Component Estimate is proposed as the design matrix X is ill-conditioned in the linear regression model. Under the criteria of mean square error, and certain conditions, R - s shrunken principal component estimate is better than Ridge - type principal component estimate and Stein - type principal component estimate. The admissibility, numerical stability and the superiority under Pitman＇s measure of closeness is achieved.