Robust $M$-Estimation of Scatter Matrices via Precision Structure Shrinkage
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917277458235392 |
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| author | Nikai, Soma Goto, Yuichi Tsukuda, Koji |
| author_facet | Nikai, Soma Goto, Yuichi Tsukuda, Koji |
| contents | Maronna's and Tyler's $M$-estimators are among the most widely used robust estimators for scatter matrices. However, when the dimension of observations is relatively high, their performance can substantially deteriorate in certain situations, particularly in the presence of clustered outliers. To address this issue, we propose an estimator that shrinks the estimated precision matrix toward the identity matrix. We derive a sufficient condition for its existence, discuss its statistical interpretation, and establish upper and lower bounds for its additive finite sample breakdown point. Numerical experiments confirm the robustness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11099 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust $M$-Estimation of Scatter Matrices via Precision Structure Shrinkage Nikai, Soma Goto, Yuichi Tsukuda, Koji Methodology Statistics Theory Computation 62H12, 62F35 Maronna's and Tyler's $M$-estimators are among the most widely used robust estimators for scatter matrices. However, when the dimension of observations is relatively high, their performance can substantially deteriorate in certain situations, particularly in the presence of clustered outliers. To address this issue, we propose an estimator that shrinks the estimated precision matrix toward the identity matrix. We derive a sufficient condition for its existence, discuss its statistical interpretation, and establish upper and lower bounds for its additive finite sample breakdown point. Numerical experiments confirm the robustness of the proposed method. |
| title | Robust $M$-Estimation of Scatter Matrices via Precision Structure Shrinkage |
| topic | Methodology Statistics Theory Computation 62H12, 62F35 |
| url | https://arxiv.org/abs/2601.11099 |