Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption

There has been a surge of interest in developing robust estimators for models with heavytailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two types of robust estimators, the ridge logtruncated M-estimator and the elastic net log-truncated M-estimator. The first estimator is applied to convex regressions such as quantile regression and generalized linear models, while the other one is applied to high dimensional non-convex learning problems such as robustness of log-truncated estimations over standard estimations.