Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910453244887040 |
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| author | Liu, Bin Qi, Zhengling Zhang, Xinsheng Liu, Yufeng |
| author_facet | Liu, Bin Qi, Zhengling Zhang, Xinsheng Liu, Yufeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_11532 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach Liu, Bin Qi, Zhengling Zhang, Xinsheng Liu, Yufeng Methodology 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. |
| title | Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach |
| topic | Methodology |
| url | https://arxiv.org/abs/2207.11532 |