Rank-Based Sparse Regression in Principal Components Space under Measurement Error
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918430100160512 |
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| author | Feng, Long Wang, Xiaoyi Zhou, Le |
| author_facet | Feng, Long Wang, Xiaoyi Zhou, Le |
| contents | We study high-dimensional regression in principal components space when the predictors are observed with additive measurement error and the response errors may be heavy-tailed. The starting point is the $\ell_1$-penalized principal-components estimator of Song and Zou (2026), which enjoys a blessing-of-dimensionality phenomenon under predictor contamination but senstive for heavy-tailed data or outliers. We replace the squared loss by a Wilcoxon-type rank loss and then apply a one-step adaptive reweighting scheme to reduce the shrinkage bias of the initial $\ell_1$ fit. The resulting procedure combines robustness to heavy-tailed response errors with the contamination geometry induced by the empirical principal-components basis. Our main theorem gives a prediction bound for the fixed-$λ$ second-stage fitted mean. Simulations show that the rank-based procedure is competitive under Gaussian noise and substantially more stable under heavy-tailed errors, especially when predictor contamination is present. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04807 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rank-Based Sparse Regression in Principal Components Space under Measurement Error Feng, Long Wang, Xiaoyi Zhou, Le Methodology We study high-dimensional regression in principal components space when the predictors are observed with additive measurement error and the response errors may be heavy-tailed. The starting point is the $\ell_1$-penalized principal-components estimator of Song and Zou (2026), which enjoys a blessing-of-dimensionality phenomenon under predictor contamination but senstive for heavy-tailed data or outliers. We replace the squared loss by a Wilcoxon-type rank loss and then apply a one-step adaptive reweighting scheme to reduce the shrinkage bias of the initial $\ell_1$ fit. The resulting procedure combines robustness to heavy-tailed response errors with the contamination geometry induced by the empirical principal-components basis. Our main theorem gives a prediction bound for the fixed-$λ$ second-stage fitted mean. Simulations show that the rank-based procedure is competitive under Gaussian noise and substantially more stable under heavy-tailed errors, especially when predictor contamination is present. |
| title | Rank-Based Sparse Regression in Principal Components Space under Measurement Error |
| topic | Methodology |
| url | https://arxiv.org/abs/2604.04807 |