Robust change point detection for high‐dimensional linear models with tolerance for outliers and heavy tails

Abstract This article focuses on detecting change points in high‐dimensional linear regression models with piecewise constant regression coefficients, moving beyond the conventional reliance on strict Gaussian or sub‐Gaussian noise assumptions. In the face of real‐world complexities, where noise often deviates into uncertain or heavy‐tailed distributions, we propose two tailored algorithms: a dynamic programming algorithm (DPA) for improved localization accuracy, and a binary segmentation algorithm (BSA) optimized for computational efficiency. These solutions are designed to be flexible, catering to increasing sample sizes and data dimensions, and offer a robust estimation of change points without requiring specific moments of the noise distribution. The efficacy of DPA and BSA is thoroughly evaluated through extensive simulation studies and application to real datasets, showing their competitive edge in adaptability and performance.