# Scale calibration for high-dimensional robust regression

arXiv: https://arxiv.org/abs/1811.02096 · HTML: https://mlsanity.com/paper/1811.02096/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2018.

## Built on by (most cited first, 6 of 6)

- [A Piecewise Lyapunov Analysis of Sub-quadratic SGD: Applications to Robust and Quantile Regression](https://mlsanity.com/paper/2504.08178/) (2025)
- [Heavy Lasso: sparse penalized regression under heavy-tailed noise via data-augmented soft-thresholding](https://mlsanity.com/paper/2506.07790/) (2025)
- [Robust Variable Selection and Estimation Via Adaptive Elastic Net S-Estimators for Linear Regression](https://mlsanity.com/paper/2107.03325/) (2021)
- [Robust High-Dimensional Regression with Coefficient Thresholding and its Application to Imaging Data Analysis](https://mlsanity.com/paper/2109.14856/) (2021)
- [The Adaptive τ-Lasso: Robustness and Oracle Properties](https://mlsanity.com/paper/2304.09310/) (2023)
- [Exponential Lasso: robust sparse penalization under heavy-tailed noise and outliers with exponential-type loss](https://mlsanity.com/paper/2511.15332/) (2025)

## Abstract (arXiv)

We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber M-estimator, for which theoretical results on estimation error have recently been proposed in high-dimensional statistics literature. However, the variance of the error term in the linear model is intricately connected to the optimal parameter used to define the shape of the Huber loss. Our main idea is to use an adaptive technique, based on Lepski's method, to overcome the difficulties in solving a joint nonconvex optimization problem with respect to the location and scale parameters.