摘要
考虑相依回归(SUR)模型yi=Xiβi_ei,i=1,2,…,m,Eei=0,i,j=1;2,…m,其中yi和ei是n×1维随机向量,Xi是n×pi已知矩阵,βi是pi×1维参数向量,∑=(σij)m×m>0.文中给出了两个概念:独立贡献和简洁估计.主要结果是如下五种叙述等价:(1)SUR模型具有独立贡献;(2)βi的BLUE是简洁估计;(3)协方差改进估计是BLUEZ(4)βi的BLUE具有形式其中,j=1,2,…,m;(5)PkNiNj=0,i≠j,k,I,j=1,2,…。
Consider the seemingly unrelated ragression (SUR) model where yi, ei: n×1 are random vectors, Xi: n×pi is a known matrix, βi: pi×1 is a parameter vector, ∑= (σij): m×m > 0. We give two notions, Independent Contribution and Simple Estimator, in this paper. The main result is that the following five statements are equivalent:(1) SUR model has independent contribution.(2) BLUE of βi is a simple estimator.(3) The covariance improved estimator is BLUE.(4) BLUE of βi has the form
出处
《系统科学与数学》
CSCD
北大核心
1996年第4期301-310,共10页
Journal of Systems Science and Mathematical Sciences
基金
山东省自然科学基金
关键词
相依回归模型
回归参数
回归模型
两步估计
Seemingly unrelated regression model
regressional coefficient
independent Contribution
simple estimator
two-step estimator.