Abstract Many modern datasets are collected automatically and thus easily contaminated by outliers. This has led to a renewed interest in robust estimation, including new notions of robustness such as adversarial contamination the data. However, most estimation methods designed for specific model. Notably, many were proposed recently obtain estimators linear models, or generalized few developed...

We present a new method for robust high-dimensional linear regression when the scale parameter of additive errors is unknown. The proposed estimator based on penalized Huber M-estimator, which theoretical bounds estimation error have recently been in statistics literature. However, variance term model intricately connected to optimal used define shape loss. Our main idea use an adaptive techniq...

Functional quadratic regression models postulate a polynomial relationship rather than linear one between scalar response and functional covariate. As in regression, vertical especially high–leverage outliers may affect the classical estimators. For that reason, providing reliable estimators such situations is an important issue. Taking into account model equivalent to of same order principal c...