ArticleBiometrika2017
Robust reduced-rank regression.
Article in Biometrika, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- Robust Transfer Learning for High-Dimensional GLM UsingStatistics in medicine · 2025Article
- Low-rank regression models for multiple binary responses and their applications to cancer cell-line encyclopedia data.Journal of the American Statistical Association · 2024Article
- Sparse Reduced Rank Huber Regression in High Dimensions.Journal of the American Statistical Association · 2023Article
- Sparse Single Index Models for Multivariate Responses.Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America · 2021Article
- A Tailored Multivariate Mixture Model for Detecting Proteins of Concordant Change Among Virulent Strains ofJournal of the American Statistical Association · 2018Article
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Authors and funding
2 authors.
Funding
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Abstract
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint modelling and outlier detection. The problem is formulated as a regularized multivariate regression with a sparse mean-shift parameterization, which generalizes and unifies some popular robust multivariate methods. An efficient thresholding-based iterative procedure is developed for optimization. We show that the algorithm is guaranteed to converge and that the coordinatewise minimum point produced is statistically accurate under regularity conditions. Our theoretical investigations focus on non-asymptotic robust analysis, demonstrating that joint rank reduction and outlier detection leads to improved prediction accuracy. In particular, we show that redescending [Formula: see text]-functions can essentially attain the minimax optimal error rate, and in some less challenging problems convex regularization guarantees the same low error rate. The performance of the proposed method is examined through simulation studies and real-data examples.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.