高维分布的非参数变点检测与推断
Nonparametric Change-Point Detection and Inference for High-Dimensional Distributions
- Tiangong University（天津工业大学）
- Nankai University（南开大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对高维分布中均值协方差不变但分布改变且受影响坐标未知的问题，提出基于标准秩比较的非参数变点检测方法，结合和/最大扫描与柯西组合适应稀疏性，无需矩假设，可扩展多变点检测，模拟和实际数据验证有效。
AI中文摘要：
高维分布可能在均值或协方差不变的情况下发生变化，而受影响坐标的数量往往未知。我们提出了非参数方法，通过边际分布的标准秩比较来同时应对这两个挑战。和扫描与最大扫描分别针对密集和稀疏变化，而柯西组合则适应未知的稀疏性。这些方法不需要边际矩假设，并通过野生二元分割扩展到多变点检测。在弱相依高斯copula模型下，我们建立了渐近零分布、渐近独立性、检测一致性和定位保证。模拟实验表明，该方法在形状和尾部变化（包括保持前两阶矩的备择假设）上具有竞争力的表现。基因表达和传感器数据的应用展示了结合密集与稀疏证据的实际益处。
英文摘要：
High-dimensional distributions can change without altering means or covariances, while the number of affected coordinates is often unknown. We propose nonparametric procedures that address both challenges through standardized rank comparisons of marginal distributions. Sum and maximum scans target dense and sparse changes, and a Cauchy combination adapts to unknown sparsity. The procedures require no marginal moment assumptions and extend to multiple-change detection through wild binary segmentation. Under a weakly dependent Gaussian copula model, we establish asymptotic null distributions, asymptotic independence, detection consistency, and localization guarantees. Simulations demonstrate competitive performance for changes in shape and tails, including alternatives that preserve the first two moments. Applications to gene expression and sensor data illustrate the practical benefits of combining dense and sparse evidence.
