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arXiv · 2207.11532

Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach

Bin Liu·Zhengling Qi·Xinsheng Zhang·Yufeng Liu
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Abstract

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.

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Bin Liu, Zhengling Qi, Xinsheng Zhang, Yufeng Liu. 2024-05-21. Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach. https://arxiv.org/abs/2207.11532

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