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

Let X1, …,Xn 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 c[Xbar]+ d admissible is studied here.