View Submission - EcoSta2022

A0678
**Title: **A statistical learning assessment of Huber regression
**Authors: **Yunlong Feng - The State University of New York at Albany (United States) **[presenting]**

Qiang Wu - Middle Tennessee State University (United States)

**Abstract: **Some theoretical understanding of Huber regression from a statistical learning viewpoint will be reported. The focus will be on the following two aspects: (1) how Huber regression estimators learn the conditional mean function and (2) why they work in the absence of light-tailed noise assumptions. To answer the two questions, we will report the following efforts we made. First, the usual risk consistency property of Huber regression estimators, which is usually pursued in learning, cannot guarantee their learnability in mean regression; second, it is argued that Huber regression should be implemented in an adaptive way to perform mean regression, implying that one needs to tune the scale parameter in accordance to the sample size and the moment condition of the noise; third, with an adaptive choice of the scale parameter, Huber regression estimators can be mean regression calibrated under ($1+\epsilon$)-moment conditions ($\epsilon>0$), and exponential-type convergence rates for Huber regression estimators can be established.

Qiang Wu - Middle Tennessee State University (United States)