Adaptive Huber Regression

By Qiang Sun, Wen-Xin Zhou, Jianqing Fan. Journal of the American Statistical Association, 2017

359 citations recorded by the source corpus.

Abstract Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our theoretical framework deals with heavy-tailed distributions with bounded th moment for any . We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when , the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime and the transition is smooth and optimal. In addition, we extend the methodology to allow both heavy-tailed predictors and observation noise. Simulation studies lend further support to the theory. In a genetic study of cancer cell lines that exhibit heavy-tailedness, the proposed methods are shown to be more robust and predictive. Supplementary materials for this article are available online.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dcf586a27e6237e031efd699b9cd7e6ca89a3d02

Citations in the corpus