标题： 改进对两个正态总体有序限制标准差的正幂估计 显示英文标题

标题： Improved estimation of the positive powers ordered restricted standard deviation of two normal populations

摘要： 本文研究了两个正态总体在均值具有一定限制条件下的有序约束标准差的正幂的分量估计问题。 我们提出了几个在一般尺度不变碗状损失函数下改进的估计量。 此外，我们提出了一类改进的估计量。 已经证明该类估计量的边界估计量是一个广义贝叶斯估计量。 作为应用，得到了关于二次损失、熵损失和一个对称损失函数的改进估计量。 我们进行了大量的蒙特卡洛模拟来研究和比较所提出的估计量的风险性能。 最后，给出了一个实际数据分析以说明我们的发现。 显示英文摘要

摘要： The present manuscript is concerned with component-wise estimation of the positive power of ordered restricted standard deviation of two normal populations with certain restrictions on the means. We propose several improved estimators under a general scale invariant bowl-shaped loss function. Also, we proposed a class of improved estimators. It has been shown that the boundary estimator of this class is a generalized Bayes. As an application, the improved estimators are obtained with respect to quadratic loss, entropy loss, and a symmetric loss function. We have conducted extensive Monte Carlo simulations to study and compare the risk performance of the proposed estimators. Finally, a real life data analysis is given to illustrate our findings.