The Linear Admissble Estimators for A Linear Function of Two Scale Parameters

LetY=(y₁,y₂)',y₁,y₂≥0;EY=β=（β₁,β₂）', VarY=k diag（β₁²,β₂²）,β∈（R⁺）² is a parameter vector , where K＞ 0 is constant and R⁺=（0,∞）. We estimate L'β, where L'=（L₁,L₂）'. Under squared-error loss function, a sufficient and necessary condition that a linear estimator is L-admissible about L'β is gained, where L=A'Y:A=（a₁,a₂）' is a 2×1 constant vector, a₁,a₂ ≥ 0).