发表机构
Pediatric Research Institute; Guangzhou Women and Children’s Medical Center; Guangzhou Medical University（儿科研究所; 广州市妇女儿童医疗中心; 广州医科大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对多元尺度与位置-尺度模型，通过坐标置换扩大变换群并利用中位数引理，构造了Pitman最近等变估计量，在模拟和实际数据中优于极大似然与贝叶斯估计。
AI 中文摘要
对于具有独立分量的多元尺度模型和位置-尺度模型，我们将Zhou和Nayak（2012）的单变量结果进行推广，并在广义Pitman接近准则下推导出最优等变估计量。我们首先通过一个反例表明，在多元情形下，等变估计量类内部的Pitman接近比较不具有传递性，因此一般而言不存在Pitman最近等变估计量。随后，我们通过坐标置换来扩大变换群——等价地，在Berger（1985）的形式等变原则下，对同构的分量问题施加该原则，这符合Robbins（1951）复合决策理论中可分离规则的精神——并证明在由此产生的受限类中，最优性得以恢复。基于严格凸损失的一个多元中位数引理，进而给出了尺度参数、尺度参数的幂以及位置参数的显式Pitman最近等变估计量，它们由任意给定等变估计量的中位数调整版本给出。我们详细研究了多元均匀分布和多元正态分布的应用。针对Rayleigh分布以及具有Rayleigh分量寿命的竞争风险模型的蒙特卡罗实验证实，所提出的估计量在Pitman接近准则下优于极大似然估计量和贝叶斯估计量，而一个关于球轴承失效时间的真实工业数据集则说明了该方法在实践中的可行性。
英文摘要
For multivariate scale and location--scale models with independent components, we extend the univariate results of Zhou and Nayak (2012) and derive optimum equivariant estimators under the generalized Pitman closeness criterion. We first show, by a counterexample, that in the multivariate case the Pitman closeness comparison within the class of equivariant estimators is not transitive, so that a Pitman closest equivariant estimator does not exist in general. We then enlarge the transformation group by the coordinate permutations---equivalently, impose the formal equivariance principle of Berger (1985) across isomorphic component problems, in the spirit of the separable rules of Robbins' (1951) compound decision theory---and show that within the resulting restricted class an optimum is restored. A multivariate median lemma based on strictly convex losses then yields explicit Pitman closest equivariant estimators of the scale parameters, powers of the scale parameters, and the location parameters, given by median-adjusted versions of any given equivariant estimator. Applications to the multivariate uniform and multivariate normal distributions are worked out in detail. Monte Carlo experiments for the Rayleigh distribution and for a competing risks model with Rayleigh component lifetimes confirm that the proposed estimators dominate the maximum likelihood and Bayes estimators under the Pitman closeness criterion, and a real industrial data set on ball bearing failure times illustrates the feasibility of the method in practice.
