SOME RESULTS ON ADMISSIBILITY OF SIMULTANEOUS ESTIMATES OF REGRESSION COEFFICIENTS AND ERROR VARIONCE Under Matrix Loss Function
J Chen · 1992
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~20 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