Adaptive Ridge-Regularized Hotelling Change-Point Tests for Functional Data

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.