关于广义压缩最小二乘估计的注记

本文研究了广义压缩最小二乘估计（ＧＳＬＳＥ）的一些性质，给出了它的均方误差（ＭＳＥ）的一个无偏估计量（ＵＥ），采用极小该ＵＥ的方法确定了ＧＳＬＳＥ的参数选取公式，并把这个统一化的方法应用于广义岭估计，岭估计、Ｍａｓｓｙ主成分估计、Ｓｔｅｉｎ型压缩估计以及根方有偏估计等，从而得到了它们的一种选取参数的方法，最后，结合Ｈａｌｄ实例进行比较分析，结果表明，本文的方法是实用的，有效的。

A Note on the Generalized Shrunken Least Squares Estimator

This paper investigates some properties about the Generalized Shrunken Least Squares Estimator(GSLSE),and gives a Unibiased Estimator (UE) of Mean Squares Error(MSE) of GSLSE. By minimizing the UE mentioned above,a formula of choosing parameters of GSLSE is deterimined. We may apply this unitary method to the Generalized Ridge Estimator,the Ridge Estimator, Massy Principal Components Estimator, Stein Shrunken Estimator and Root Biased Estimator and so on,to obtain one method of chooosing parameters of them. Finally, through comparative analysis between linear biased estimators with the help of the practical example of Hald data,the results indicates that the method presented in this paper is useful and effective.