广义岭估计的新定义及其性质

THE NEW DEF IN IT ION OF GENERAL IZED RIDGE EST IMATOR AND ITS PROPERT IES

本文提出了一类新估计:(k)=(x′x+k)^(-1)x′y,k=diag(k_1,k_2,…k_p),它是岭估计的自然推广,但不同于Hoerl和Kennard在[1]中提出的广义岭估计。我们证明了存在k>o使(k)的均方误差小于最小二乘估计=(x′x)^(-1)x′y的均方误差,并且(k)是β的可容许估计。

In fhis paper,We propose a new class estimators of β:(K)=(X'X+K)^-1X'Y,K=diag(k_1,…k_p),and it is a natural generalized of kidge estimator,But it is different from fhe Generatized kidge Estimator by Hoerl and Kennard putting forward. it is proved fhat fhere is a K>O to make lees MSE of (K)than MSE of LS estimate.Besides,(K)is an admissible estimate of β.