观测向量的变换对广义线性模型参数估计的影响

The Influence to Parameter Estimation in a General Linear Regression Model with Linear Transformations

中文关键词:  广义Gauss-Markoff模型  线性变换  非负定离差阵．

英文关键词:general Gauss-Markoff model  linear transformation  nonnegative definite dispersion matrix.

中文摘要:

      本文一般地考察了观测向量Ｙ用线性变换ＦＹ代替对广义线性模型Ｙ＝Ｘβ＋ε的系数估计的影响，得到了由变换引起的方差增量公式，并由此得到了一个可估子空间，当且仅当其中元素的估计优良性不因观测向量的变化而改变，这一结果推广了文献［１］的结果．

英文摘要:

      For an arbitrary rank general Gauss Markoff model Y=Xβ+μ,μ∽(0,Σ) , where Σ is a nonnegative ddefinite matrix, the effect of transforming the observable vector Y to FY is analyzed with respect to the variance of the Best Linear Unbiased Estimator (BLUE) of C′β . It is shown that there exists an estimable subspace S in which the BLUE of C′β can be get as a function of FY . The result obtained in [1] is generalized in this paper.