标题： 两个正态总体的正次幂有序限制标准差的改进估计 显示英文标题

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

摘要： 本文手稿关注在均值具有某些限制的情况下，两个正态总体的有序受限标准差的正幂的分量估计。 我们提出了一些在一般尺度不变碗状损失函数下的改进估计量。 此外，我们提出了一个改进估计量的类。 已经证明该类的边界估计量是一个广义贝叶斯估计量。 作为应用，根据二次损失、熵损失和对称损失函数得到了改进估计量。 我们进行了广泛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，给出一个实际数据的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.