On the admissibility of c[Xbar] + d with respect to the linex loss function

Let X₁, …,X_n be a random sample from a normal distribution with mean θ and variance σ² The problem is to estimate θ with loss function L(θ,e) = v(e-θ) where v(x) = b(exp(ax)-ax-l) and where a, b are constants with b>0, a¦0. Zellner (1986), showed that Xbar] ? σ²a/2n dominates Xbar] and hence Xbar] is inadmissible. The question of what values of c and d render cXbar]+ d admissible is studied here.