Location-Adaptive Change-Point Testing for Time Series
时间序列的位置自适应变点检验AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究时间序列变点检验，并将检验功效与变点位置联系起来，因此对应时间序列与结构变化方向。
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时间序列的位置自适应变点检验
- 研究问题
- 当变点位于序列早期或晚期时，自归一化检验为何可能损失功效，能否通过调整所用样本改善这一问题？
- 方法与思路
- 作者提出剔除远离候选变点的样本，通过最优子样本选择构造位置自适应的自归一化统计量，并讨论向其他参数检验扩展。
- 材料陈述的贡献
- 摘要称新检验改善既有方法的功效并保持令人满意的检验尺寸，且所提样本选择策略可用于其他依赖累积和过程的方法。
- 阅读关注点
- 应核对最优样本选择的目标与约束、边界变点的处理、依赖结构要求，以及尺寸和功效比较所覆盖的设计。
- 阅读边界
- 所据为 arXiv 预印本，同行评审或期刊接收未核实；摘要未说明最优性的具体条件、临界值构造及改善幅度。
原文摘要
We propose a location-adaptive self-normalization (SN) based test for change points in time series. The SN technique has been extensively used in change-point detection for its capability to avoid direct estimation of nuisance parameters. However, we find that the power of the SN-based test is susceptible to the location of the break and may suffer from a severe power loss, especially when the change occurs at the early or late stage of the sequence. This phenomenon is essentially caused by the unbalance of the data used before and after the change point when one is building a test statistic based on the cumulative sum (CUSUM) process. Hence, we consider leaving out the samples far away from the potential locations of change points and propose an optimal data selection scheme. Based on this scheme, a new SN-based test statistic adaptive to the locations of breaks is established. The new test can significantly improve the power of the existing SN-based tests while maintaining a satisfactory size. It is a unified treatment that can be readily extended to tests for general quantities of interest, such as the median and the model parameters. The derived optimal subsample selection strategy is not specific to the SN-based tests but is applicable to any method that relies on the CUSUM process, which may provide new insights in the area for future research.