This paper investigates the problem of estimating the larger location parameter of two general location families from a decision-theoretic perspective. In this estimation problem, we use the criteria of minimizing the risk function and the Pitman closeness under a general bowl-shaped loss function. Inadmissibility of a general location and equivariant estimators is provided. We prove that a natural estimator (analogue of the BLEE of unordered location parameters) is inadmissible, under certain conditions on underlying densities, and propose a dominating estimator. We also derive a class of improved estimators using the Kubokawa's IERD approach and observe that the boundary estimator of this class is the Brewster-Zidek type estimator. Additionally, under the generalized Pitman criterion, we show that the natural estimator is inadmissible and obtain improved estimators. The results are implemented for different loss functions, and explicit expressions for the dominating estimators are provided. We explore the applications of these results to for exponential and normal distribution under specified loss functions. A simulation is also conducted to compare the risk performance of the proposed estimators. Finally, we present a real-life data analysis to illustrate the practical applications of the paper's findings.

翻译：本文从决策理论角度研究了两个一般位置族中较大位置参数的估计问题。在该估计问题中，我们采用在一般碗状损失函数下最小化风险函数和皮特曼接近度作为准则。给出了广义位置和等变估计量的不可容许性。我们证明了在潜在密度的特定条件下，自然估计量（无序位置参数BLEE的类似物）是不可容许的，并提出了一个占优估计量。我们还利用Kubokawa的IERD方法推导了一类改进估计量，并观察到该类估计量的边界估计量是Brewster-Zidek型估计量。此外，在广义皮特曼准则下，我们证明了自然估计量是不可容许的，并获得了改进估计量。针对不同损失函数实现了这些结果，并给出了占优估计量的显式表达式。我们探讨了这些结果在指定损失函数下对指数分布和正态分布的应用。还进行了模拟研究以比较所提出估计量的风险性能。最后，我们通过真实数据分析来阐述本文研究结果的实际应用。