一般增长曲线模型回归系数的一种可容许有偏估计

A Class of Biased Admissibility Estimate of Regression Coefficients in General Growth Curve Model

对于线性回归模型:Y=Xβ+,εE(s)=0,cov(ε)=σ2v,v>0,文献[1]给出了有偏估计sβ*=(XTV-1X+sI)-1(XTV-1Y+β*),其中s>0为参数,β表示线性回归模型的广义最小二乘估计,文献[2]中已经证明了sβ*的可容许性并且有很多优良性质.作者用类似的方法证明在一般增长曲线模型下该有偏估计仍具有许多优良性质并证明其在均方意义下是可容许的.

In the linear regression model： Y = Xβ＋ε,E （s） = 0, cov（ε） = σ^2v,v 〉 0, reference [ 1 ] presented a biased estimate：βx^＊ = （X^TV^-1 ＋sI）^-1 （X^TV^-1Y＋β^＊ ） , where s 〉 0 was a parameter and β was the generalized least squares estimate. In reference [ 2 ],βs^＊ proved to be an admissible estimate with many good characters. Proved that βs^＊ was an admissible estimate with many good characters in the general growth curve model in a similar way.