# Adaptive Huber Regression

@article{Sun2017AdaptiveHR, title={Adaptive Huber Regression}, author={Qiang Sun and Wen-Xin Zhou and Jianqing Fan}, journal={Journal of the American Statistical Association}, year={2017}, volume={115}, pages={254 - 265} }

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…

## 150 Citations

### Adaptive Huber Regression on Markov-dependent Data.

- Computer ScienceStochastic processes and their applications
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### A pr 2 01 9 Adaptive Huber Regression on Markov-dependent Data

- Computer Science
- 2019

The results show that the Markov dependence impacts on the adaption of the robustification parameter and the estimation of regression coefficients in the way that the sample size should be discounted by a factor depending on the spectral gap of the underlying Markov chain.

### Support estimation in high-dimensional heteroscedastic mean regression

- Mathematics, Computer Science
- 2020

This paper considers a linear mean regression model with random design and potentially heteroscedastic, heavy-tailed errors, and investigates support estimation in this framework, using a strictly convex, smooth variant of the Huber loss function with tuning parameter depending on the parameters of the problem, as well as the adaptive LASSO penalty for computational efficiency.

### User-Friendly Covariance Estimation for Heavy-Tailed Distributions

- MathematicsStatistical Science
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This work introduces element-wise and spectrum-wise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix and proposes tuning-free procedures that automatically calibrate the tuning parameters.

### Robust Fused Lasso Penalized Huber Regression with Nonasymptotic Property and Implementation Studies

- Computer Science
- 2022

An adaptive Huber regression for robust estimation and inference is proposed, in which, the fused lasso penalty is used to encourage the sparsity of the coeﬃcients as well as theSparsity of their diﬀerences, i.e., local constancy of the Coe-Sciencen proﬁle.

### Robust Variable Selection and Estimation Via Adaptive Elastic Net S-Estimators for Linear Regression

- Mathematics
- 2021

Heavy-tailed error distributions and predictors with anomalous values are ubiquitous in high-dimensional regression problems and can seriously jeopardize the validity of statistical analyses if not…

### Tuning-Free Huber Regression : A Non-asymptotic Perspective of Robustness

- Computer Science, Mathematics
- 2018

A new data-driven tuning scheme to choose the robustification parameter for Huber-type sub-Gaussian estimators in three fundamental problems: mean estimation, linear regression and sparse regression in high dimensions is proposed.

### Robust regression with covariate filtering: Heavy tails and adversarial contamination

- Mathematics, Computer ScienceArXiv
- 2020

This work shows how to modify the Huber regression, least trimmed squares, and least absolute deviation estimators to obtain estimators which are simultaneously computationally and statistically efficient in the stronger contamination model.

### Robust High-dimensional Tuning Free Multiple Testing

- Mathematics, Computer Science
- 2022

This study develops Berry-Esseen inequality and Cram´er type moderate deviation for the HL estimator based on newly developed non-asymptotic Bahadur representation, and builds data-driven conﬁdence intervals via a weighted bootstrap approach and convincingly shown that the resulting tuning-free and moment-free methods control false discovery proportion at a prescribed level.

### High-dimensional robust approximated M-estimators for mean regression with asymmetric data

- Computer ScienceJ. Multivar. Anal.
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