多元线性模型中的有偏估计

THE BIASED ESTIMATES IN MULTIVARIATE LINEAR MODEL

刘金山在1999年给出了多元线性模型参数分量βi和参数矩阵B的有偏估计β1=(X'X)-1YCi,i=1,…,m和B=(β1,β2,…,βm)以及βi的性质.本文从另一角度得到了同样的估计,证明了刘金山文中所给的两个检验是UMP检验,估计βi是βi的线性可容许估计,证明了B不是B的可容许估计,由此给出了两种改进估计.

Paper[1] gives the biased estimats βi = (X' X)-1X'YCi (i = 1,2, … ,m) and B = (β1,β2, … ,βm) of parameter components βi and parameter matrix B,and the properties of βi.This paper makes the same estimation fromanother angle. It proves that two tests in paper [1] are UMP-tests and that the estimate βi is a linear admissible estimates of βi. It also proves that B is not an admissible estimate of B. As a result of these, we give two kinds of improved estimates.