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

Consider linear model Y=（Y₁,…,Y_n）＇=Xβ+ε=Xβ+（ε₁,…,ε_n)',whereX be a n×p known design matrix, β=（β₁,…,β_p)', σ²＞0 be unknown parameters, ε₁,…,ε_n be independent, E_εi=E_εi³=0,E_ε4²=σ²,E_εi⁴=3σ⁴,i=1,2,…,n. In this parper, we give out Some necessary and Sufficient conditions for estimate（AY,Y'BY） of （Sβ, σ²） to be admissible in the class of \mathscrC \times \mathscrD=\left\\left(C Y, Y^\prime D Y\right)\right.:C be a ×n constant matrix,D be a n×n non-negative definite constant matrix under matrix \operatornameloss\binomd_1-S \betad_2-\sigma^2\binomd_1-S \betad_2-\sigma^2^\prime or \binom\fracd_1-S \beta\sigma\fracd_2-\sigma^2\sigma^2\binom\fracd_1-S \beta\sigma\fracd_2-\sigma^2\sigma^2^\prime.