Inference for change points in high-dimensional data via selfnormalization
基于自归一化的高维数据变点推断AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究高维变点检验与定位，并扩展到弱依赖时间序列，直接对应结构变化和时间序列方向。
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基于自归一化的高维数据变点推断
- 研究问题
- 如何对高维序列中的均值变化进行检验与定位，并在独立观测和弱时间依赖下构造适合稠密备择的程序？
- 方法与思路
- 作者结合U统计量与自归一化构造检验，对时间依赖情形引入截尾参数，并结合野生二分分割估计多个变点。
- 材料陈述的贡献
- 摘要称，独立情形检验无需调参，依赖情形使用截尾；作者推导原假设及备择下极限分布，并报告模拟竞争力。
- 阅读关注点
- 应核对维数与样本量关系、稠密备择范围、时间依赖条件和截尾选择，以及多变点分割程序的定位保证。
- 阅读边界
- 仅据版本未注明的OpenAlex索引摘要，具体条件和模拟数值未提供；无需调参的陈述不能延伸到依赖数据情形。
原文摘要
This article considers change-point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on U-statistic in Chen and Qin (Ann. Statist. 38 (2010) 808–835) and utilizes the self-normalization principle (Shao J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 343–366; Shao and Zhang J. Amer. Statist. Assoc. 105 (2010) 1228–1240). Our test targets dense alternatives in the high-dimensional setting and involves no tuning parameters. To extend to change-point testing for high-dimensional time series, we introduce a trimming parameter and formulate a self-normalized test statistic with trimming to accommodate the weak temporal dependence. On the theory front we derive the limiting distributions of self-normalized test statistics under both the null and alternatives for both independent and dependent high-dimensional data. At the core of our asymptotic theory, we obtain weak convergence of a sequential U-statistic based process for high-dimensional independent data, and weak convergence of sequential trimmed U-statistic based processes for high-dimensional linear processes, both of which are of independent interests. Additionally, we illustrate how our tests can be used in combination with wild binary segmentation to estimate the number and location of multiple change points. Numerical simulations demonstrate the competitiveness of our proposed testing and estimation procedures in comparison with several existing methods in the literature.