Invariance of Estimator of Scale Parameter under a Class of Symmetric Loss

For scale-parameter family c(x,n)η-νe-T(x)/η,we dealt with the property of the Bayes estimator and the admissible estimator of η=τr with the theory of intergral transformation,under the function of symmetric entropy loss L(η,d)=ν(η/d+d/η-2),for a random sample of size n arising from scale-parameter population {(1/τ) f(x/τ),τ0}.We have proved the invariance of the two estimators in one-one mapping.