TWIN：用于在线变点检测的双窗口检查方法
TWIN: Two window inspection for online change point detection
AI总结：
提出基于双窗口检查方案（TWIN）的序贯变点检验方法，通过对数检测延迟和自归一化技术显著提升检测性能，并在COVID19数据监测中验证了其实时应用价值。
摘要：
我们提出了一类新的序贯变点检验方法，既适用于均值参数的变化，也适用于整体分布函数的变化。该方法论建立在双窗口检查方案（TWIN）之上，该方案将数据聚合为对称样本并应用强加权以增强统计性能。该检测器产生对数而非多项式的检测延迟，与最先进的替代方法相比，这代表了实质性的减少。即使对于现有方法表现最差的晚变化，延迟仍然很短。此外，新程序在广泛的局部替代类别中也比现有方法获得了更高的功效。对于均值变化，我们进一步引入了检测器的自归一化版本，该版本自动消除时间依赖性，从而无需估计冗余参数。我们方法的优势得到了渐近理论、模拟以及对COVID19数据监测应用的支持。在此，与新病毒变体相关的结构性断点几乎被我们的新程序立即检测到。这表明其对未来流行病的实时监测具有潜在价值。在数学上，我们的方法由部分和过程全局连续模的新指数矩界支撑，这可能具有独立于变点检验之外的意义。
英文摘要：
We propose a new class of sequential change point tests, both for changes in the mean parameter and in the overall distribution function. The methodology builds on a two-window inspection scheme (TWIN), which aggregates data into symmetric samples and applies strong weighting to enhance statistical performance. The detector yields logarithmic rather than polynomial detection delays, representing a substantial reduction compared to state-of-the-art alternatives. Delays remain short, even for late changes, where existing methods perform worst. Moreover, the new procedure also attains higher power than current methods across broad classes of local alternatives. For mean changes, we further introduce a self-normalized version of the detector that automatically cancels out temporal dependence, eliminating the need to estimate nuisance parameters. The advantages of our approach are supported by asymptotic theory, simulations and an application to monitoring COVID19 data. Here, structural breaks associated with new virus variants are detected almost immediately by our new procedures. This indicates potential value for the real-time monitoring of future epidemics. Mathematically, our approach is underpinned by new exponential moment bounds for the global modulus of continuity of the partial sum process, which may be of independent interest beyond change point testing.
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