High-Dimensional Change-Point Detection via Angular Kernel Statistics

A new statistical framework for detecting distributional shifts in high-dimensional data has been proposed, targeting the challenging high-dimensional, low sample size regime where traditional methods often fail. The method, detailed in a preprint posted to arXiv on May 25, 2026, introduces a dimension-averaged angular kernel scan statistic [1]. It is designed to operate in the high-dimensional, low sample size (HDLSS) setting, where the number of variables far exceeds the number of observations [2]. The framework is fully nonparametric, requiring no hyperparameter tuning, and remains well-defined without assuming finite marginal moments, making it suitable for heavy-tailed or contaminated distributions [2]. For offline analysis of a single change point, the author, Jyotishka Ray Choudhury, derives an exact population mean factorization into a universal deterministic shape function and a scalar signal factor [2]. The work also characterizes the null covariance structure and establishes an HDLSS multivariate central limit theorem under cross-coordinate mixing, enabling plug-in Gaussian calibration and asymptotic type-I error control [2]. The detection scale is shown to reach a local rate of d^{-1/2} [2]. The procedure is further extended to a fixed-window sequential monitoring scheme for high-dimensional streaming data, with theoretical guarantees on average run length calibration and worst-case expected detection delay [2]. Simulation studies reported in the paper demonstrate accurate change detection and localization in settings where moment-based or hyperparameter-sensitive alternatives become unreliable [2]. Change-point detection is a long-standing problem in statistics, but the HDLSS regime presents unique difficulties because standard covariance estimation breaks down when the dimension grows faster than the sample size. The proposed angular approach sidesteps this by aggregating bounded one-dimensional angular discrepancies across coordinates, avoiding the need to estimate high-dimensional covariance structures directly [2]. The method's reliance on angular discrepancies echoes broader mathematical traditions where angular or directional statistics are used to handle scale-invariant comparisons, though the specific application to change-point detection in the HDLSS regime is novel [2]. The preprint is available on arXiv under the statistics methodology section [1].