We study change-point detection for high-dimensional data in regimes where inference must be performed from small batches of observations. Our primary focus is the high-dimensional, low sample size (HDLSS) regime, where the sequence length is fixed while the ambient dimension diverges. We propose a dimension-averaged angular kernel scan framework for detecting marginal distributional shifts. The statistic aggregates bounded one-dimensional angular discrepancies across coordinates, yielding a fully nonparametric, hyperparameter-free, and moment-agnostic estimator that remains well-defined without specifying, estimating, or assuming finite marginal moments, for example under heavy-tailed or contaminated distributions. For the offline single-change problem, we derive an exact population mean factorization into a universal deterministic shape function and a scalar signal factor, characterize the null covariance structure up to a scalar long-run variance factor, and establish an HDLSS multivariate central limit theorem under cross-coordinate mixing. These results lead to plug-in Gaussian calibration, asymptotic type-I error control, and power and localization guarantees, including a $d^{-1/2}$ local detection scale. We further extend the offline procedure to a fixed-window sequential monitoring procedure for high-dimensional streaming data, and obtain ARL calibration and worst-case EDD bounds. Simulation studies demonstrate that the proposed method can accurately detect and localize changes in challenging HDLSS and streaming settings where moment-based or hyperparameter-sensitive procedures may be unreliable.

翻译：我们研究在高维数据场景下需从少量观测批次进行推断的变点检测问题。主要关注高维低样本量（HDLSS）场景，其中序列长度固定而环境维度发散。提出一种维度平均的角核扫描框架用于检测边际分布偏移。该统计量通过聚合坐标间有界一维角差异，构建完全非参数、无超参数且不依赖矩的估计量——即使数据存在重尾或污染分布等情形，也无需指定、估计或假设有限边际矩即可明确定义。针对离线单变点问题，我们推导出精确的总体均值分解为通用确定性形状函数与标量信号因子，刻画了零假设协方差结构（至标量长期方差因子），并建立了跨坐标混合下的HDLSS多元中心极限定理。这些结果支撑了插件式高斯校准、渐近第一类错误控制、功效与定位保障（包括$d^{-1/2}$局部检测尺度）。进一步将离线流程扩展为面向高维流数据的固定窗序贯监测程序，获得平均运行长度校准与最坏情形期望检测延迟界。仿真研究表明，在基于矩或超参数敏感方法可能失效的HDLSS与流数据挑战场景下，所提方法能准确检测并定位变化点。