多元线性模型广义岭型预测的最优性判别

The optimality criterion of generalized ridge prediction in the multivariate linear model

对多元线性模型有偏估计的预测问题,利用矩阵不等式的性质,提出判别最优线性无偏预测、岭型预测和广义岭型预测最优性的一个Ri(.)准则,找到了广义岭型预测在该准则下,比最优线性无偏预测优越的充要条件,及在矩阵迹意义下优于最优线性无偏预测、岭型预测的充分条件,为多元线性模型两类预测量的最优性判别问题提供了一种新诊断方法。

Aiming at the prediction issue of the biased estimation of the multivariate linear model, The rule R^（-） is presented to distinguish the superiority among the best linear unbiased prediction, the ridge prediction and the gen- eralized ridge prediction. And it obtain an necessary and sufficient condition of the superiority between the general- ized ridge prediction and the best linear unbiased prediction under the rule R1 （·） and the two sufficient condition of the generalized ridge prediction superior to the ridge prediction and the best linear unbiased prediction under the rule based on the nature of the matrix trace. It provides a new diagnosis method for the distinguishing problem of the two kinds of predictions of the multivariate linear model.