A robust and efficient tail-adaptive approach for change-point detection in semiparametric models

Structural breaks frequently arise in economic policy evaluation, biomedical monitoring, and other dynamic systems, posing substantial challenges for partially linear models (PLMs) that contain nonparametric nuisance components. This paper develops a unified tail-adaptive CUSUM framework for structural break testing and estimation in PLMs. The proposed methodology integrates cross-fitted semiparametric composite quantile regression with a weighted CUSUM process, allowing robust inference under heterogeneous and heavy-tailed error distributions. A key theoretical contribution is the establishment of a uniform oracle equivalence result, showing that the feasible plug-in CUSUM process converges uniformly to its oracle linear-model counterpart over the time index. This equivalence provides the theoretical foundation for valid tail-adaptive testing and multiplier bootstrap inference in high-dimensional settings. We further establish non-asymptotic localization bounds, showing that the proposed estimator attains the optimal rate up to logarithmic factors. The procedure is implemented within a seeded binary segmentation scheme to accommodate multiple change-points. Simulation studies and an empirical application to energy policy data demonstrate the effectiveness and robustness of the proposed method.

Recommended citation: Chen W, Chen Y, Jing B, Zhou W, and Hu Y. (2026). "A robust and efficient tail-adaptive approach for change-point detection in semiparametric models." SCIENCE CHINA Mathematics. 69.
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