回归系数的stein型主成分估计

Combining stein and Principal Components Estimate of Regression Coefficient

对于设计阵Ｘ呈病态的线性回归模型，本文提出了一种新的关于回归系数的有偏估计─ｓｔｅｉｎ型主成分估计，并在均方误差意义下，论证了在一定条件下ｓｔｅｉｎ型主成分估计优于主成分估计，因此也优于ｓｔｅｉｎ型ＯＬＳ估计与ＯＬＳ估计，最后，我们又对偏参数的存在性，最优性进行了讨论，并得出了一些重要结论．

In this paper,we propos a new biased estimate-the SPE(stein-type principal-components estiimate)-to the coefficient of regression in leinear regression model as the design matrix is ill-conditioned.under the critcira of mean square error,and certain conditions, we obtain that SPE improves the Princing-comvponents estimate,therefore,It improves stein-type OLS estimates and OLS estimate.Finally,we discuss the existence,the optima property of the biased coefficient,and get some important results.