Universal Domination and Stochastic Domination: Estimation Simultaneously Under a Broad Class of Loss Functions
普遍支配与随机支配：广泛损失函数下的同时估计比较AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要属于损失函数、随机序与收缩估计的通用决策理论，未明确对应所列细分领域。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
普遍支配与随机支配：广泛损失函数下的同时估计比较
- 研究问题
- 当损失函数难以精确指定时，能否在所有随欧氏估计误差单调增加的损失下同时比较估计量，并识别支配关系？
- 方法与思路
- 作者将上述损失类下的普遍支配联系到误差距离的随机序，并分别研究多元 t 分布与正态模型中的收缩估计量。
- 材料陈述的贡献
- 摘要称，两种支配标准等价；t 模型的结论随维数变化，而正态模型中的正部 James–Stein 估计不具这种普遍支配。
- 阅读关注点
- 应核对损失函数类与随机序的精确定义、t 模型的维数分界，以及正态模型缩小损失类后能获得哪些支配结论。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要，不能把平方损失下的改进推广为普遍支配；具体估计量和适用条件需查阅原文。
原文摘要
In Wald's statistical decision theory, the criterion of domination (or uniform betterness) is defined with respect to a specific loss. In practice, however, the exact form of a loss function is difficult to specify. Hence, it is important to study the domination criterion simultaneously under a class of loss functions. In this paper we focus on estimation problems. We mainly investigate the possibility of domination simultaneously under the class of loss functions $L(|\theta - \delta|)$, where $L$ is an arbitrary nondecreasing function. As usual, $\theta$ and $\delta$ (both in $p$-dimensional Euclidean space $R^p$) are, respectively, the unknown parameter of nature and the statistician's estimate. Domination simultaneously under this class of losses is called universal domination under Euclidean error. Several theoretical questions are resolved in this paper. In particular the criterion of universal domination is shown to be equivalent to the criterion of stochastic domination that compares the estimators by the stochastic ordering of their Euclidean distances from the estimators to the true parameter. Concrete results about universal domination relating to the usual estimator are also established. In particular when $X - \theta$ has a $p$-variate $t$ distribution, and $p = 1, 2$, there exists no estimator for $\theta$ that universally dominates $X$; however, for $p \geq 3$, estimators (of the type of James-Stein positive part estimators) that universally dominate $X$ are specified. When $X$ has a $p$-variate normal distribution with mean $\theta$ and identity covariance matrix, we show that for any dimension $p$, no James-Stein positive part estimators universally dominate $X$. However, under slightly smaller classes of losses, some James-Stein positive part estimators are shown to simultaneously dominate $X$. These hitherto unstudied losses are bounded and fairly practical.