Estimating positive powers of ordered standard deviations of two normal populations

The present manuscript concerns component-wise estimation of the positive powers of the ordered restricted standard deviations for two normal populations under certain restrictions on the means. We obtain sufficient conditions to prove the dominance of equivariant estimators under scale-invariant strictly convex loss functions. Consequently, we propose various estimators that dominate the best affine equivariant estimator (BAEE). Furthermore, we derive a generalized Bayes estimator. As an application, we derive improved estimators for four special loss functions: quadratic, entropy, symmetric, and linex. An extensive Monte Carlo simulation is conducted to compare the risk performance of the proposed estimators. Finally, we provide a real data analysis for implementation purposes.