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arXiv · 2604.04807

Rank-Based Sparse Regression in Principal Components Space under Measurement Error

Long Feng·Xiaoyi Wang·Le Zhou
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Abstract

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-$\lambda$ 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.

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Long Feng, Xiaoyi Wang, Le Zhou. 2026-04-06. Rank-Based Sparse Regression in Principal Components Space under Measurement Error. https://arxiv.org/abs/2604.04807

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