High-dimensional changepoint estimation with heterogeneous missingness
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AI 根据所提供的论文材料归类：摘要直接研究高维时间序列中的稀疏同步均值变点及定位误差，属于结构变化与时间序列方法。
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异质缺失下的高维变点估计
- 研究问题
- 高维时间序列仅有部分坐标发生同步均值变化，且各坐标观测概率不同时，如何利用稀疏信号准确定位变点？
- 方法与思路
- 作者提出 MissCUSUM 变换，通过针对稀疏结构的惩罚优化寻找投影方向，再用投影序列绝对值的峰值估计变点位置。
- 材料陈述的贡献
- 摘要称，信号强度按观测概率加权后决定误差界，理论区分噪声与缺失误差，并以估计下界说明方法达到相差对数因子的最优性。
- 阅读关注点
- 核对缺失机制、稀疏性与均值变化设定、投影优化和调参方法，以及高概率误差界与最优性下界对应的参数空间。
- 阅读边界
- 所据为 arXiv 预印本，同行评审及期刊接收未核实；摘要未列出缺失依赖等完整条件，最优性结论不能外推至任意缺失或变点机制。
原文摘要
We propose a new method for changepoint estimation in partially-observed, high-dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first methodological contribution is to introduce a 'MissCUSUM' transformation (a generalisation of the popular Cumulative Sum statistics), that captures the interaction between the signal strength and the level of missingness in each coordinate. In order to borrow strength across the coordinates, we propose to project these MissCUSUM statistics along a direction found as the solution to a penalised optimisation problem tailored to the specific sparsity structure. The changepoint can then be estimated as the location of the peak of the absolute value of the projected univariate series. In a model that allows different missingness probabilities in different component series, we identify that the key interaction between the missingness and the signal is a weighted sum of squares of the signal change in each coordinate, with weights given by the observation probabilities. More specifically, we prove that the angle between the estimated and oracle projection directions, as well as the changepoint location error, are controlled with high probability by the sum of two terms, both involving this weighted sum of squares, and representing the error incurred due to noise and the error due to missingness respectively. A lower bound confirms that our changepoint estimator, which we call 'MissInspect', is optimal up to a logarithmic factor. The striking effectiveness of the MissInspect methodology is further demonstrated both on simulated data, and on an oceanographic data set covering the Neogene period.