In many real life situations, prior information about the parameters is available, such as the ordering of the parameters. Incorporating this prior information about the order restrictions on parameters leads to more efficient estimators. In the present communication, we investigate estimation of the ordered scale parameters of two shifted exponential distributions with unknown location parameters under a class of bowl-shaped loss functions. We have proved that the best affine equivariant estimator (BAEE) is inadmissible. Various non smooth and smooth estimators has been obtained which improve upon the BAEE. In particular we have derived the improved estimators for some well known loss functions. Finally numerical comparison is carried out to compare the risk performance of the proposed estimators.

在许多现实生活中，有关参数的先验信息是可用的，例如参数的排序。结合这些关于参数顺序限制的先验信息可以得到更有效的估计器。在目前的通信中，我们研究了在一类碗形损失函数下对位置参数未知的两个移位指数分布的有序尺度参数的估计。我们已经证明了最佳仿射等变估计量 (BAEE) 是不可接受的。已经获得了改进 BAEE 的各种非平滑和平滑估计量。特别是我们已经为一些众所周知的损失函数推导出了改进的估计量。最后进行数值比较以比较所提出的估计器的风险性能。