回归系统广义岭型主成分两步估计的优良性质

The good nature of two-step estimation of generalized ridge and principal components of regression system

针对两步估计问题,在设计阵成病态的情形下,探讨了残差变量相关的多个方程回归系统如何转化为一般线性模型;与有偏估计相结合,得到该方程系统未知参数的估计模型——m个相关方程回归系统的广义岭型主成分有偏两步估计;证明了该估计在相对效率的意义上比一般的两步估计、主成分两步估计、岭型主成分两步估计的效率高。

Aiming at two-step estimation, the way of the multiple equation regression system transposing to a general linear model is discussed. Combining with the biased two-step estimation, a model for the estimation of unknown parameters of the regression system is obtained when its design matrix is pathological. It is proved that the biased two-step estimation is more efficient in the sense of the relative efficiency compared with the general two-step estimation, the two-step estimation of the principal component and the two-step estimation of ridge and principal components.