摘要
对于一般的正态线性回归模型Ｙ＝Ｘβ＋ε，ε～Ｎｎ（０，σ∑）本文采用极小化均方程差的方法得到了回归系数的一种非线性有偏估计，即广义Ｓｔｅｉｎ估计，给出了它的偏差及其均方误差的渐近展开式，并且在均方误差意义下，当误差干扰充分小（σ→０）时，给出了该估计优于ＢＬＵ估计的渐近充要条件。
For a general normal liner regression models: Y = Xβ + ε,ε- Nn(0,σ2E) , a nonlinear biased estimator of regression coefficients i.e. a generalized Stein estimator is obtained with the methods of minimizing the MSE of a linear estimator in this paper , it's asymptotic expansions of bias and MSE are derived , and when error disturbances are sufficiently small (σ→0) , the asymptotic necessary and sufficient condition is also derived for this estimator to dominate the BLUE under the MSE criterion .
关键词
广义
斯坦因估计
线性回归
a generalized Stein estimator , mean square error (MSE) , best linear unbiased estimator ( BLUE ) .
