AI 中文总结
该研究针对高维时间序列变点检测，提出基于多尺度统计量与赫尔德-高斯近似的方法，通过模拟和加州野火空气污染数据验证了其有效性。
AI 中文摘要
我们提出了用于高维时间序列变点检测的新型推断工具，讨论了两类不同的统计应用：第一，对传入数据流的序贯变点检验；第二，对多个变点的回溯定位，且置信区间需满足全局控制的误差水平。检验统计量基于最大范数构建，以针对稀疏且异步的变点产生检验效能。两类问题均通过相关的多尺度统计量解决，该统计量会在多个不同分辨率层级上搜索数据中的变点。对于固定维度，我们的统计方法可通过传统的赫尔德不变性原理验证。本文中，我们提出了高维情形下的类似物：赫尔德-高斯近似，其可（粗略地）解释为高维部分和过程的赫尔德范数对应的高斯近似。此类近似的应用范围超出了变点检测，还可用于其他问题，例如高维情形下的平稳性检验。我们通过模拟研究评估了有限样本性能，并将其应用于加利福尼亚州野火导致的空气污染问题，该污染在一组测量站之间异步发生。
英文摘要
We present new inference tools for change point detection in high-dimensional time series. We discuss two distinct statistical applications: First, sequential change point testing in an incoming data-stream. Second, retrospective localization of multiple changes, with confidence intervals at a globally controlled error level. Test statistics are built on the maximum norm to generate power against sparse and asynchronous changes. Both problems are tackled by related multiscale statistics that search for changes in the data at many different levels of resolution. For fixed dimension, our statistical approaches can be validated using traditional Hölderian invariance principles. In this paper, we present the high-dimensional analogue: Hölder-Gauss-approximations, which can be (roughly) interpreted as the Gaussian approximation for a Hölder-norm of the high-dimensional partial sum process. Such approximations are of interest beyond change point detection and can be used for other problems such as for stationarity testing in high dimensions. We evaluate finite-sample performance in a simulation study and give an application to air contamination due to wildfires in California, which occurs asynchronously across a panel of measuring stations.
