系统误差模型下估计的性质

The Natures of the Estimates in the Model Containing the Systematic Error

在含有系统误差的线性回归模型Yn=Xnβ+Iη+e里,研究了η和β估计的性质.当随机误差和设计矩阵满足一定的条件时,分别给出了∧η(n)和c′∧β(n)弱相合性的证明.在η和d′β各自对应的线性无偏估计类中,证明了∧(ηn)和d′∧β(n)是唯一具有最小方差的估计.

In the linear regression model Yn=Xnβ＋Iη＋e containing the systematic error,the properties of the estimate of η and β are studied.When the random error and the design matrix meet certain conditions,the proofs of the weak consistency of η∧（n） and c′β∧（n） are given respectively.In the corresponding category of linear unbiased estimates of η and d′β,it is proved that the η∧（n） and d′β∧（n） the are the only estimates with minimum variances.