Dimension-agnostic Change Point Detection
不依赖维度选择的变点检测AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究多元时间序列中单个均值结构变化的检测和检验。
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不依赖维度选择的变点检测
- 研究问题
- 对于低、中、高维多元时间序列，能否构造统一检验检测单个均值变点，使零假设极限分布不随维度或截面依赖强度改变？
- 方法与思路
- 作者提出面向单个均值变点的维度无关检验，分析零假设极限分布与大样本功效，并通过 Monte Carlo 和真实数据展示。
- 材料陈述的贡献
- 摘要称，检验的极限零分布对维度及截面依赖强度保持相同，有限样本结果支持理论，并建议作为不同维度变点检测的基准。
- 阅读关注点
- 应核对允许的时间依赖与截面依赖条件、维度增长范围、变点位置限制，以及功效对变化幅度和变化方向的敏感性。
- 阅读边界
- 所给版本为 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未说明具体正则条件，结论针对单个均值变点而非任意变化。
原文摘要
Change point testing for high-dimensional data has attracted a lot of attention in statistics and machine learning owing to the emergence of high-dimensional data with structural breaks from many fields. In practice, when the dimension is less than the sample size but is not small, it is often unclear whether a method that is tailored to high-dimensional data or simply a classical method that is developed and justified for low-dimensional data is preferred. In addition, the methods designed for low-dimensional data may not work well in the high-dimensional environment and vice versa. In this paper, we propose a dimension-agnostic testing procedure targeting a single change point in the mean of a multivariate time series. Specifically, we can show that the limiting null distribution for our test statistic is the same regardless of the dimensionality and the magnitude of cross-sectional dependence. The power analysis is also conducted to understand the large sample behavior of the proposed test. Through Monte Carlo simulations and a real data illustration, we demonstrate that the finite sample results strongly corroborate the theory and suggest that the proposed test can be used as a benchmark for change-point detection of time series of low, medium, and high dimensions.