AI 中文总结
该研究针对函数型时间序列均值变化检测与定位问题，提出统一的岭正则化霍特林框架，通过基展开、协方差估计、岭正则化及相关统计量组合等方法，在多种条件下建立了检验性质，模拟和实证表明其有限样本性能良好。
AI 中文摘要
我们提出了一个统一的岭正则化霍特林框架，用于检测和定位函数型时间序列中的均值变化。通过不断增长的基展开将函数观测值转换为高维得分向量，其长期协方差通过基于边缘校正差分的程序进行估计。岭正则化在谱衰减下稳定推断。一个明确的局部功效公式表明，使功效最大化的岭取决于变化的未知谱方向。因此，我们通过柯西变换组合一族岭累积和统计量，并直接从它们的联合加权桥极限校准总体。对于多个变化，我们将局部最大岭统计量嵌入到野生二元分割过程中，然后进行局部细化。在温和条件下，我们建立了所提出检验的有效性、局部功效、一致性和定位性质。在多变化设置中，该过程一致地恢复变化数量并均匀估计其位置。该框架适用于弱相依和非高斯函数误差。模拟和两个实证应用证明了所提方法良好的有限样本性能。
英文摘要
We propose a unified ridge-regularized Hotelling framework for detecting and locating mean changes in functional time series. A growing basis expansion converts the functional observations into high-dimensional score vectors. Their long-run covariance is estimated by an edge-corrected difference-based procedure. Ridge regularization stabilizes inference under spectral decay. An explicit local-power formula shows that the power-maximizing ridge depends on the unknown spectral orientation of the change. We therefore combine a family of ridge CUSUM statistics by a Cauchy transform and calibrate the aggregate directly from their joint weighted-bridge limit. For multiple changes, we embed local maximum-ridge statistics in a wild binary segmentation procedure, followed by local refinement. Under mild conditions, we establish the validity, local power, consistency, and localization properties of the proposed tests. In the multiple-change setting, the procedure consistently recovers the number of changes and uniformly estimates their locations. The framework accommodates weak dependence and non-Gaussian functional errors. Simulations and two empirical applications demonstrate the favorable finite-sample performance of the proposed methods.
