The Bayes Estimator of the Positive Restricted Parameter under the Power-Power Loss with an Application

The proposed power-power loss function which has balanced convergence rates or penalties for its argument too large and too small, has all the seven properties listed in this paper, and thus it is recommended to use for the positive restricted parameter space. We then calculate the Bayes estimator, the posterior risk, the integrated risk, and the Bayes risk of the parameter under the power-power loss function. After that, we analytically calculate these quantities under a hierarchical normal and normal-inverse-gamma model. Finally, the numerical simulations exemplify our theoretical studies.