一般线性模型下删除观测值的影响

Effect of Deleting an Observation on Estimator in General Lnear Models

在一般情形下，给出了在模Ｍ＝｛Ｙ，Ｘβ，σ２Ｖ｝与删除第ｉ个观测值后得到的模型Ｍｄ＝｛Ｙｄ，Ｘｄβ，σ２Ｖｄ｝下Ｘｄβ的最佳线性无偏估计差的表达式．得到了二者相等的充要条件，给出了在模型Ｍｄ下Ｘｄβ的最小二乘估计是Ｍ下Ｘｄβ的最佳线性无偏估计的充要条件，以及Ｍｄ下σ２的最小范数二次无偏估计是Ｍ下σ２的最小范数二次无偏估计的充要条件．

A formula for the difference between the BLUEs of Xβ under M={Y,Xβ,σ 2V} and the BLUEs of X dβ under M d={Y d,X dβ,σ 2V d} is given.Further the necessary and sufficient conditions for the equality of above two estimators are established, and the necessary and sufficient conditions for the equality of the OLSE of X dβ under M d and the BLUEs of X dβ under M are established.It also give the necessary and sufficient condition for the NINQUE of σ 2 under M d to be the MINQUE of σ 2 under M.