Recent advances have greatly facilitated the collection of high-dimensional data in many fields. Often the dimension of the data is much larger than the sample size, the so-called high dimension, low sample size setting. One important research problem is how to develop efficient change-point detection procedures for this new setting. Thanks to their simplicity of computation, interpoint distance-based procedures provide a potential solution to this problem. However, most of the existing distance-based procedures fail to fully utilise interpoint distances, and as a result, they suffer significant loss of power. In this paper, we propose a new asymptotic distribution-free distance-based change-point detection procedure for the high dimension, low sample size setting. The proposed procedure is proven to be consistent for detecting both location and scale changes and can also provide a consistent estimator for the change-point. Our simulation study and real data analysis show that it significantly outperforms the existing methods across a variety of settings.

中文翻译：

---

基于点间距离的高维数据渐近无分布变点检测

最近的进展极大地促进了许多领域的高维数据的收集。往往数据的维度远大于样本量，即所谓的高维度、低样本量设置。一个重要的研究问题是如何为这种新环境开发有效的变化点检测程序。由于计算简单，基于点间距离的程序为这个问题提供了一个潜在的解决方案。然而，大多数现有的基于距离的程序未能充分利用点间距离，因此，它们遭受了严重的功率损失。在本文中，我们为高维、低样本量设置提出了一种新的基于渐近分布的基于距离的变化点检测程序。所提出的程序被证明对于检测位置和尺度变化是一致的，并且还可以为变化点提供一致的估计器。我们的模拟研究和真实数据分析表明，它在各种设置下都明显优于现有方法。