A statistical learning assessment of Huber regression

As one of the triumphs and milestones robust statistics, Huber regression plays an important role in inference estimation. It has also been finding a great variety applications machine learning. In parametric setup, it extensively studied. However, statistical learning context where function is typically learned nonparametric way, there still lack theoretical understanding how estimators learn conditional mean why works absence light-tailed noise assumptions. To address these fundamental questions, this paper conducts assessment from viewpoint. First, we show that usual risk consistency property estimators, which usually pursued learning, cannot guarantee their learnability regression. Second, argue should be implemented adaptive way to perform regression, implying needs tune scale parameter accordance with sample size moment condition noise. Third, choice parameter, demonstrate can asymptotic calibrated under (1+?)-moment conditions (?>0) on distribution. Last but not least, same conditions, establish almost sure convergence rates for estimators. Note accommodate special case response variable possesses infinite variance so established justify robustness feature above senses, present study provides systematic justifies merits terms