AI 中文总结
该研究针对高维序列位置变化检测提出椭圆正则化霍特林检验（ERHT），通过特定方法结合稳健性与加权，建立高斯过程极限，嵌入野生二元分割，模拟显示其校准良好、功效强，还分析投资组合找出结构断点。
AI 中文摘要
我们提出了一种椭圆正则化霍特林（ERHT）程序，用于检测具有重尾、横截面相关观测值的高维序列中的位置变化。ERHT使用合并的中心空间符号协方差矩阵的岭正则化逆来对比相邻段上的空间中位数，从而将对径向变化的稳健性与依赖感知加权相结合。我们建立了单变化和多变化扫描以及在有限正则化参数集上的联合收敛的高斯过程极限。这些结果通过联合高斯极限为柯西聚合自适应检验提供了渐近精确校准，同时保证了局部功效和单变化定位。我们进一步将ERHT分数嵌入野生二元分割中，并证明了估计多个变化的数量和位置的一致性。模拟表明，ERHT通常校准良好，并且在重尾分布下具有竞争力的功效，特别是当横截面依赖性很强时。对法玛 - 法国49个行业投资组合的分析揭示了位置不稳定性的持续证据，并识别出四个结构断点。
英文摘要
We propose an elliptical regularized Hotelling (ERHT) procedure for detecting location changes in high-dimensional sequences with heavy-tailed, cross-sectionally dependent observations. ERHT contrasts spatial medians on adjacent segments using a ridge-regularized inverse of the pooled centered spatial-sign covariance matrix, thereby combining robustness to radial variation with dependence-aware weighting. We establish Gaussian-process limits for the single- and multiple-change scans and joint convergence over a finite set of regularization parameters. These results provide asymptotically exact calibration of a Cauchy-aggregated adaptive test through the joint Gaussian limit, together with guarantees for local power and single-change localization. We further embed the ERHT score in wild binary segmentation and prove consistency for estimating the number and locations of multiple changes. Simulations show that ERHT is generally well calibrated and delivers competitive power under heavy-tailed distributions, particularly when cross-sectional dependence is substantial. An analysis of the Fama--French 49 industry portfolios reveals persistent evidence of location instability and identifies four structural breaks.
