多元线性模型中随机回归系数和参数的线性估计在线性估计类中的可容许性(Ⅰ)

Admissibility of Linear Estimate of Stochastic Regression Coefficients and Parameters in a Multivariable Linear Model of the Class of the Linear Estinates

考虑多元线性模型Ｙ＝ＸＢ＋Ｅ，其中Ｙ是可观测的ｎ×ｍ矩阵，Ｂ和Ｅ分别为不可观测的ｐ×ｍ和ｎ×ｍ随机矩阵，ＥＢＥ＝ＡαＯ，ＣｏｖＢＥ＝Ｖ；Ｘ，Ａ，Ｖ均为已知矩阵，≥０，Ｖ≥０，是已知矩阵或未知的参数矩阵，α∈Ｒｋ×ｍ为未知的参数矩阵。本文在矩阵损失函数：（ｄ－Ｓα－ＱＢ）′（ｄ－Ｓα－ＱＢ）下给出了Ｓα＋ＱＢ的估计ＬＹ（ＬＹ＋ｃ）在齐次线性估计类（线性估计类）中可容许的充要条件，从而将文献［１］［３］中得到的关于一元模型的有关结果推广到多元模型。

Consder the multivariable model Y=XB+E,where Y is an observable n×m matrix, B and E are p×m and n×m unobservable random matrices,and EB E=Aα O,C ov B E=V,and X,A,V are known matrices.α∈R k×m is a unknown matrix of parameters. Under the matrix loss functions:(d-Sα-QB)′(d-Sα-QB),the necessary and sufficient conditions for an estimate LY(LY+C) of Sα+QB to be admissible among the class homogeneous linear estimates(linear estimates) are gained.