A Stability Framework for Parameter Selection in the Minimum Covariance Determinant Problem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915367118438400 |
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| author | Heng, Qiang Shen, Hui Lange, Kenneth |
| author_facet | Heng, Qiang Shen, Hui Lange, Kenneth |
| contents | The Minimum Covariance Determinant (MCD) method is a widely adopted tool for robust estimation and outlier detection. In this paper, we introduce MCD model selection based on the notion of stability. Our best subset method leverages prior best practices such as statistical depths for initialization and concentration steps for subset refinement. Our contribution lies in constructing a bootstrap procedure to estimate the instability of the best subset algorithm. The instability path offers insights into a dataset's inlier/outlier structure and facilitates suitable choice of the subset size. We rigorously benchmark the proposed framework against existing MCD variants and illustrate its practical utility on several real-world datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Stability Framework for Parameter Selection in the Minimum Covariance Determinant Problem Heng, Qiang Shen, Hui Lange, Kenneth Methodology Computation The Minimum Covariance Determinant (MCD) method is a widely adopted tool for robust estimation and outlier detection. In this paper, we introduce MCD model selection based on the notion of stability. Our best subset method leverages prior best practices such as statistical depths for initialization and concentration steps for subset refinement. Our contribution lies in constructing a bootstrap procedure to estimate the instability of the best subset algorithm. The instability path offers insights into a dataset's inlier/outlier structure and facilitates suitable choice of the subset size. We rigorously benchmark the proposed framework against existing MCD variants and illustrate its practical utility on several real-world datasets. |
| title | A Stability Framework for Parameter Selection in the Minimum Covariance Determinant Problem |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2401.14359 |