多元线性模型回归系数的根方估计

Root-Power Estimate of the Regression Coefficient in Multivariate Linear Model

本文采用根方估计估计多元线性模型中的回归系数B,通过根方参数k值的选取,可使(k)=Vec((k))的均方误差MSE小于β=Vec(B)的LS估计B的MSE。本文还给出了选取k值的两种方法及一个应用实例。

In this paper, root power estimate (k)=(X'X)^(k-1)X'Y, (0<k<1) of the regression coefficient B is considered in multivariate linear model. It is proved that the MSE of (k) =Vec((k)) is less than the LS estimate β~* of the β=Vec(B) by choosing the root power parameter k. Two methods (root trace, condition number) are used to evaluate the optimal k value, and an applied example is given.