Abstract: We propose a novel approach for detecting change points in high- dimensional linear regression models. Unlike previous research that relies on strict Gaussian/sub-Gaussian error assumptions and has 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 proposed method.

Key words and phrases: Binary segmentation, bootstrap, heterogeneity, multiple change points.