Robust estimation for functional quadratic regression models

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 component scores predictor processes, our proposal combines robust directions with based on bounded loss function preliminary residual scale estimator. Fisher–consistency proposed method derived under mild assumptions. Consistency, asymptotic robustness as well expression for influence related functionals when covariates have finite–dimensional expansion. The results numerical study show benefits over sample least squares considered contaminating scenarios. usefulness approach also illustrated through analysis real data set which reveals potential are removed behaves very similarly computed all data.