增加试验数据对岭估计的均方误差的影响

THE INFLUENCE OF ADDING SAMPLE DATA ON MEAN SQUARE ERROR OF RIDGE ESTIMATE

在线性模型中,对于回归系数的岭估计和广义岭估计,本文给出了选择岭参数的条件,在此条件下,岭估计和广义岭估计不仅能改善LS估计,而且增加试验数据时,它们的均方误差都会减少。同时,本文将增加试验数据换成增加附加信息,从而讨论了附加信息对混合岭估计和混合广义岭估计的影响问题。

It is reasonable to hope that the mean square error of estimation of parameters is decreased by adding sample datas in a linear model. In this paper, for Ridge estimation and Generalized Ridge estimation of regression coefficients, the conditions of choosing Ridge paraincters are presented, in which Ridge estimation and Generalised Ridge estimation not only improve LSE, but their mean square error is also decreased by adding sample datas. And then, by the replacement that the additional information take the additional sample datas place the. influence of the additinal information on Mixed Ridge estimate and Mixed Generalized Ridge estimate are discussed.