Properties of higher criticism under strong dependence
强依赖下 higher criticism 检验的性质AI 解读 ↓
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强依赖下 higher criticism 检验的性质
- 研究问题
- 在大量同时检验中检测稀疏且微弱信号时，观测之间的短程依赖和强依赖如何影响 higher criticism 的表现？
- 方法与思路
- 作者分析依赖数据下 higher criticism 的信号检测性质，并与基于信号值差分或数据最大值的方法比较。
- 材料陈述的贡献
- 摘要称短程依赖没有一阶影响；强依赖下其他方法可能更优，并用统计量仿佛仅保留大块代表观测来解释表现。
- 阅读关注点
- 应核对短程与强依赖的定义、信号稀疏程度和强度设定、性能比较标准，以及大块代表观测解释的形式化依据。
- 阅读边界
- 所给为版本未注明的 OpenAlex 索引摘要；具体依赖模型与检测条件未说明，不能将比较结论推广到所有相关数据。
原文摘要
The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each problem can be solved by conducting a large number of simultaneous hypothesis tests, the properties of which are readily accessed under the assumption of independence. In this paper we address the case of dependent data, in the context of higher criticism methods for signal detection. Short-range dependence has no first-order impact on performance, but the situation changes dramatically under strong dependence. There, although higher criticism can continue to perform well, it can be bettered using methods based on differences of signal values or on the maximum of the data. The relatively inferior performance of higher criticism in such cases can be explained in terms of the fact that, under strong dependence, the higher criticism statistic behaves as though the data were partitioned into very large blocks, with all but a single representative of each block being eliminated from the dataset.