In the usual statistical inference problem, we estimate an unknown parameter of a statistical model using the information in the random sample. A priori information about the parameter is also known in several real-life situations. One such information is order restriction between the parameters. This prior formation improves the estimation quality. In this paper, we deal with the component-wise estimation of location parameters of two exponential distributions studied with ordered scale parameters under a bowl-shaped affine invariant loss function and generalized Pitman closeness criterion. We have shown that several benchmark estimators, such as maximum likelihood estimators (MLE), uniformly minimum variance unbiased estimators (UMVUE), and best affine equivariant estimators (BAEE), are inadmissible. We have given sufficient conditions under which the dominating estimators are derived. Under the generalized Pitman closeness criterion, a Stein-type improved estimator is proposed. As an application, we have considered special sampling schemes such as type-II censoring, progressive type-II censoring, and record values. Finally, we perform a simulation study to compare the risk performance of the improved estimators

翻译：在常规的统计推断问题中，我们利用随机样本中的信息来估计统计模型的未知参数。在许多现实情境中，关于参数的先验信息也是已知的。其中一种信息是参数间的序约束。这种先验信息能够提升估计质量。本文研究了在碗状仿射不变损失函数和广义Pitman接近准则下，具有有序尺度参数的两个指数分布的位置参数的分量估计问题。我们证明了若干基准估计量，如最大似然估计量（MLE）、一致最小方差无偏估计量（UMVUE）和最佳仿射等变估计量（BAEE），都是不可容许的。我们给出了推导占优估计量的充分条件。在广义Pitman接近准则下，提出了一种Stein型改进估计量。作为应用，我们考虑了特殊抽样方案，如II型截尾、渐进II型截尾和记录值。最后，我们进行了模拟研究以比较改进估计量的风险性能。