Cellwise and Casewise Robust Multivariate Regression with Inference
Abstract
Multivariate linear regression is a fundamental statistical task, but classical estimators such as ordinary least squares are highly sensitive to outliers. These may occur as casewise outliers that affect entire observations, or as outlying cells, that are individual contaminated entries in the predictor and/or response matrix. Moreover, modern datasets frequently contain missing values and are high-dimensional. To address these challenges we propose the cellwise multivariate regression (cellMR) estimator, a robust regression method that simultaneously accommodates casewise and cellwise outliers, missing data, and high dimensionality. The approach builds on a cellwise robust covariance estimator and uses ridge regularization for numerical stability. We further introduce cellBoot, a novel bootstrap-based inference procedure tailored to the cellMR framework. Relying on indirect inference, cellBoot provides asymptotically valid confidence intervals that are robust to casewise and cellwise contamination. We derive influence functions and breakdown bounds of the regression estimator and prove the asymptotic validity of the cellBoot confidence intervals. Simulations and a real genomics application illustrate the strong finite-sample performance of the proposed methods.
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BibTeX
@misc{centofanti2026cellwise,
title = {{Cellwise and Casewise Robust Multivariate Regression with Inference}},
author = {Fabio Centofanti and Mia Hubert and Peter J. Rousseeuw},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.08002},
eprint = {2605.08002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.08002},
note = {CC0},
}
RIS
TY - UNPB
TI - Cellwise and Casewise Robust Multivariate Regression with Inference
AU - Fabio Centofanti
AU - Mia Hubert
AU - Peter J. Rousseeuw
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2605.08002
UR - https://arxiv.org/abs/2605.08002
AB - Multivariate linear regression is a fundamental statistical task, but classical estimators such as ordinary least squares are highly sensitive to outliers. These may occur as casewise outliers that affect entire observations, or as outlying cells, that are individual contaminated entries in the predictor and/or response matrix. Moreover, modern datasets frequently contain missing values and are high-dimensional. To address these challenges we propose the cellwise multivariate regression (cellMR) estimator, a robust regression method that simultaneously accommodates casewise and cellwise outliers, missing data, and high dimensionality. The approach builds on a cellwise robust covariance estimator and uses ridge regularization for numerical stability. We further introduce cellBoot, a novel bootstrap-based inference procedure tailored to the cellMR framework. Relying on indirect inference, cellBoot provides asymptotically valid confidence intervals that are robust to casewise and cellwise contamination. We derive influence functions and breakdown bounds of the regression estimator and prove the asymptotic validity of the cellBoot confidence intervals. Simulations and a real genomics application illustrate the strong finite-sample performance of the proposed methods.
ER -