论文标题
高维度的计算高效和数据自适应更改点推断
Computationally efficient and data-adaptive changepoint inference in high dimension
论文作者
论文摘要
适应各种变化模式的高维更改点推断最近受到了很多关注。我们提出了一种简单，快速但有效的方法，用于自适应更改点测试。关键观察结果是，在某些轻度条件下，基于所有维点和可能的更改点基于总体和可能的更改点的累积总和统计数据的两个统计数据是渐近独立的。因此，我们能够根据其极限null分布组合最大值和求和型统计的p值来形成新的测试。为此，我们开发了新的工具和技术，以在所有变量之间在更轻松的条件下建立最大类型统计量的渐近分布，而不是现有文献中的变量。所提出的方法易于使用，并且在计算上有效。它适应不同的变化信号的稀疏性水平，并且与我们的数值研究所揭示的那样，与现有方法相当。
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.
