标题： 计算高效且数据自适应的高维变点推断 显示英文标题

标题： Computationally efficient and data-adaptive changepoint inference in high dimension

摘要： 高维突变点推理问题近年来引起了广泛关注，这类问题旨在适应各种变化模式。我们提出了一种简单、快速且有效的自适应突变点检测方法。关键观察发现，在一些较弱的条件下，基于所有维度和可能的突变点累积和统计量的最大值和总和的两个统计量是渐近独立的。因此，我们可以根据它们的极限零分布结合最大值型和总和型统计量的p值来构建一个新的检验方法。为了实现这一点，我们开发了新的工具和技术，在比现有文献中更宽松的条件下建立了最大值型统计量的渐近分布。所提出的检验方法易于使用且计算效率高。它能够适应不同稀疏度的变化信号，并且通过我们的数值研究显示，该方法与现有的方法相比具有竞争力，甚至优于现有的方法。 显示英文摘要

摘要： High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two statistics based on aggregating cumulative sum statistics over all dimensions and possible changepoints by taking their maximum and summation, respectively, are asymptotically independent under some mild conditions. Hence we are able to form a new test by combining the p-values of the maximum- and summation-type statistics according to their limit null distributions. To this end, we develop new tools and techniques to establish asymptotic distribution of the maximum-type statistic under a more relaxed condition on componentwise correlations among all variables than that in existing literature. The proposed method is simple to use and computationally efficient. It is adaptive to different sparsity levels of change signals, and is comparable to or even outperforms existing approaches as revealed by our numerical studies.