The problem of simultaneous estimation of order restricted location parameters $\theta_1$ and $\theta_2$ ($-\infty<\theta_1\leq \theta_2<\infty$) of a bivariate location symmetric distribution, under a general loss function, is being considered. In the literature, many authors have studied this problem for specific probability models and specific loss functions. In this paper, we unify these results by considering a general bivariate symmetric model and a quite general loss function. We use the Stein and the Kubokawa (or IERD) techniques to derive improved estimators over any location equivariant estimator under a general loss function. We see that the improved Stein type estimator is robust with respect to the choice of a bivariate symmetric distribution and the loss function, as it only requires the loss function to satisfy some generic conditions. A simulation study is carried out to validate the findings of the paper. A real-life data analysis is also provided.

翻译：本文考虑在一般损失函数下，对二元位置对称分布中顺序约束的位置参数 $\theta_1$ 和 $\theta_2$（$-\infty<\theta_1\leq \theta_2<\infty$）进行同时估计的问题。文献中，许多学者针对特定概率模型和特定损失函数研究了该问题。本文通过考虑一般二元对称模型与相当一般的损失函数，统一了这些结果。我们利用Stein和Kubokawa（或IERD）技术，在一般损失函数下推导出优于任何位置等变估计量的改进估计量。我们发现，改进的Stein型估计量对二元对称分布和损失函数的选择具有鲁棒性，因为它仅要求损失函数满足某些泛化条件。通过模拟研究验证了本文的结论，并提供了实际数据分析。