随机回归系数和参数的联合估计的可容许性

ADMISSIBILITY OF SIMULTANEOUSLINEAR ESTIMATION OF STOCHASTIC REGRESSION COEFFICIENTS AND PARAMETERS

考虑一般的线性模型Ｙ＝Ｘβ＋ε，Ｙ为可观察的ｎ维向量，ε和β是不可观察的ｎ维和ｐ维随机向量；Ｅ（β）＝Ａαａ，ＶＡＲ（β）＝△≥０（或σ２△）；Ｅ（ε）＝０， ＶＡＲ（ε）＝Ｖ≥０（或σＶ）；Ｅ（εβ′）＝０；Ｘ，Ａ，△，Ｖ是已知矩阵；α∈Ｒｋ，σ＞０皆为未知多数。本文在矩阵损失函数下，给出了（Ｓα，Ｑβ）的估计（Ｌ１Ｙ，Ｌ２Ｙ）在齐次估计类中可容许的充要条件。

The linear model Y=Xβ+ε is considered, where Y is n-dimensional vector oboserva-tions,β is a p-dimensional vector of unobserable stochastic coefficients; E(β)=Aα, VAR (β)=△≥0(or g‘σ2△);E(ε)=0, VAR(ε)=V≥0(or σ2V);E(ε′β)=0; X,A,△ and V are known matrics; α∈Rk(α∈Rk, σ>0) is (are) parameters. Necessary and sufficients condi-tions for an estimate(L1Y,L2Y)of(Sα,Qβ)to be admissible in the class of linear estimates under the matrix loss function are given.