摘要
引进了多元线性模型中回归系数β＝Ｖｅｃ（Ｂ）的广义压缩最小二乘估计β（Ａ），讨论了它的约方误差与均方残差的性质，指出了根据均方误差准则选取Ａ值的主要缺陷，采用了一种选取Ａ值的新准则Ｑ（ｃ），它包含均方误差准则和最小二乘准则作为特例，并从理论上证明了Ｑ（ｃ）准则的优良性．
In this paper, generalized shrunken least square estimate g(A) of the regression coefficient β=Vec (B) is considered in multivariate linear regression model. The properties of MSE and MSR of the above estimate are discussed. Moreover, this paper point out that the criteria MSE for choosing matrix A of generalized shrunken least square estimate has several weaknesses. In order to overcome these weaknesses, a new family of criteria Q(c) are adopted which includes the criteria MSE and criteria LS as its special case, The good properties of criteria Q(c) are proved from theoretical points of view.
