09/10/2026 - 14:30 - ISBA C115 - 
 

Jing Zhou

(University of Manchester) 

Will give a presentation on : 

Dense High-Dimensional Huber Regression under Heteroscedasticity

Abstract: 
We study Huber regression in a heteroscedastic linear model when the number of predictors is comparable to the sample size. We show that the first-order center of the Huber estimator may contain an additional component along the direction governing the conditional scale, and we derive the resulting asymptotic center and normalized risk. A conditional Huber-centering condition is shown to be sufficient for this nuisance-direction component to vanish. The analysis uses matrix approximate message passing to track the regression and scale directions simultaneously. The talk will introduce the statistical mechanism behind the result, explain the connection with classical sandwich variance formulas, and outline how state evolution yields an exact high-dimensional characterization. No prior knowledge of approximate message passing is required.