矩阵损失下回归系数和误差方差的联合估计的可容许性的几个结果

SOME RESULTS ON ADMISSIBILITY OF SIMULTANEOUS ESTIMATES OF REGRESSION COEFFICIENTS AND ERROR VARIONCE Under Matrix Loss Function

设有线性模型:Y=(Y_1,…,Y_n)＇=Xβ+ε=Xβ+(ε_1,…,ε_n)＇,其中X:n×p已知,β=(β_1,…,β_p)＇未知,ε_1,…,ε_n独立,E_(ε_i)=E_(ε_i^3)=0,E_(ε_4~2)=σ~2,F_(ε_i^4)=3σ~4,i=1,2,…,n,0<σ~2<∞,σ~2未知。在矩阵损失下,我们考虑(Sβ,σ~2)的联合估计(AY,Y＇BY)在估计类×={(CY,Y＇DY):C为m×n的常数阵,D≥0为n×n的常数阵中的可容许性,得到了(AY,Y＇BY)为(Sβ,σ~2)的可容许估计的一些充分条件和必要条件。

Consider linear model Y=(Y_1, …, Y_n)′=Xβ_δ+(δ_1, …, δ_n)′ where X be a n×p known design matrix, β=(β_1, …,δ_p)′, σ~2>0 be unknown parameters, δ_1, …, δ_n be independent, Eδ_i)=Eδ_4~3=0, Eδ_1~2=σ~2, Eδ_1~4=3σ~4, i=1, 2, … , n. In this parper, we give out Some necessary and Sufficient conditions for estimate(AY, Y'BY) of (Sβ, σ~2) to be admissible in the class of ×={(CY, Y′DY):σ be am×n constant matrix, D be a n×n n non-negative definite constant matrix under matrix