发表机构
University of Twente; Centrum Wiskunde & Informatica (CWI)（特温特大学; 数学与计算机科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对数据最终用途未知时的统计约简问题，研究两类边界情形，证明了极小充分统计量为一对一映射时无平凡约简，给出自适应采样高斯流的最优样本量及下界。
AI 中文摘要
假设在对数据进行约简或收集时，数据的最终用途是未知的。本注记考虑两个简单的边界情形。在有限统计实验中，一个统计量对每个后续的有限决策问题都保持贝叶斯风险，当且仅当它是充分统计量。因此，当极小充分统计量是一对一映射时，对所有后续决策问题的精确保持不允许进行非平凡的约简。我们接着考虑从m个独立高斯流中进行自适应采样，其中外部查询仅在采样停止后才指定要分类的坐标。在逐坐标误差控制下，最优对称平均样本量恰好是单坐标最优值的m倍。测度变换论证根据二元相对熵给出了对应的逐点下界。
英文摘要
Suppose that the eventual use of data is not known when the data are reduced or collected. This note considers two simple boundary cases. In a finite statistical experiment, a statistic preserves the Bayes risk for every finite later decision problem if and only if it is sufficient. Hence, when the minimal sufficient statistic is one-to-one, exact preservation of all later decision problems permits no nontrivial reduction. We then consider adaptive sampling from $m$ independent Gaussian streams when an external query specifies the coordinate to be classified only after sampling stops. Under coordinatewise error control, the optimal symmetric average sample size is exactly $m$ times the one-coordinate optimum. A change-of-measure argument gives the corresponding pointwise lower bound in terms of binary relative entropy.
