多元广义Stein估计及其优良性  

Multivariate Generalized Stein Estimate and Its Optimality

作　　者：蔡新民[1] 方兴[1] 黄养新[1] 

机构地区：[1]武汉理工大学

出　　处：《武汉理工大学学报》2001年第9期87-89,共3页Journal of Wuhan University of Technology

摘　　要：对于多元正态线性模型 ,采用极小化均方误差的方法得到了回归系数的一种非线性有偏估计 ,即多元广义Stein估计 ,给出了它的偏差及其均方误差的渐近展开式。在均方误差意义下 ,当误差干扰充分小 (σ→ 0 )时 ,得到了该估计优于 LFor multivariate normal linear model, a nonlinear biased estimate of regression coefficients, which is multivariate generalized Stein estimate, is presented by the method of minimizing mean square error of linear estimate in this paper. Its asymptotic expansions of bias and mean square error are derived, and when error disturbance is sufficiently small, the asymptotic necessary and sufficient conditions are also shown for this estimate to dominate the best linear unbiased estimate under the mean square error criterion.

关 键 词：多元线性模型 均方误差 多元广义 STEIN估计 偏差 回归分析 

分 类 号：O212.1[理学—概率论与数理统计]