  We propose a novel approach for detecting change points in high-dimensional
linear regression models. Unlike previous research that relied on strict
Gaussian/sub-Gaussian error assumptions and had prior knowledge of change
points, we propose a tail-adaptive method for change point detection and
estimation. We use a weighted combination of composite quantile and least
squared losses to build a new loss function, allowing us to leverage
information from both conditional means and quantiles. For change point
testing, we develop a family of individual testing statistics with different
weights to account for unknown tail structures. These individual tests are
further aggregated to construct a powerful tail-adaptive test for sparse
regression coefficient changes. For change point estimation, we propose a
family of argmax-based individual estimators. We provide theoretical
justifications for the validity of these tests and change point estimators.
Additionally, we introduce a new algorithm for detecting multiple change points
in a tail-adaptive manner using the wild binary segmentation. Extensive
numerical results show the effectiveness of our method. Lastly, an R package
called ``TailAdaptiveCpt" is developed to implement our algorithms.
