用于相关性和趋势的重叠窗口测试
Overlapping window tests for correlation and trend
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中文总结 AI 辅助
本文针对依赖性和趋势检测构建分析重叠滑动窗口统计量，利用马尔可夫链及谱结构获正交分解，给出提取增量依赖信息的方法并用于相关性和趋势检测示例，还得到增量信息定量度量，提供了设计重叠窗口测试及推导相关性质的系统方法。
中文摘要 AI 辅助
我们开发了一个通用框架，用于构建和分析用于依赖性和趋势检测的重叠滑动窗口统计量。对于固定窗口大小，重叠块形成马尔可夫链，任何中心化窗口统计量的渐近方差由该链的协方差算子确定。利用其谱结构，我们获得窗口函数空间到与不同重叠水平相关的分量的正交分解。这引出了增量依赖信息的自然概念：统计量中准确捕捉窗口扩大引入的新信息的部分。我们给出提取这些分量的明确过程，并将该方法应用于两类示例。对于相关性检测，我们研究对称多项式窗口函数并识别其信息投影部分。对于趋势检测，我们分析局部基于秩的统计量并分离最大新引入滞后的贡献。示例还表明不同统计量可能表现出不同的局部检测尺度，包括非经典的。相同观点导致增量信息的自然定量度量，可用于评估窗口大小增加时捕获的新依赖结构量，并指导尺度选择。总体而言，本文提供了一种设计重叠窗口测试并推导其渐近归一化和局部行为的系统方法。
英文摘要
We develop a general framework for constructing and analyzing overlapping sliding-window statistics for dependence and trend detection. For a fixed window size, the overlapping blocks form a Markov chain, and the asymptotic variance of any centered window statistic is determined by the covariance operator of this chain. Using its spectral structure, we obtain an orthogonal decomposition of the space of window functions into components associated with different overlap levels. This leads to a natural notion of incremental dependence information: the part of a statistic that captures exactly the new information introduced by enlarging the window. We give an explicit procedure for extracting these components and apply the method to two classes of examples. For correlation detection, we study symmetric polynomial window functions and identify their informative projected part. For trend detection, we analyze localized rank-based statistics and isolate the contribution of the largest newly introduced lag. The examples also show that different statistics may exhibit different local detection scales, including nonclassical ones. The same viewpoint leads to a natural quantitative measure of incremental information, which can be used to assess how much new dependence structure is captured as the window size increases, and to guide scale selection. Overall, the paper provides a systematic method for designing overlapping-window tests and deriving their asymptotic normalization and local behavior.
