Title: Penalized robust estimation for functional regression
Authors: Anestis Antoniadis - Universite Joseph Fourier (France)
Italia De Feis - National Research Council of Italy (Italy)
Maria Francesca Carfora - Istituto per le Applicazioni del Calcolo - CNR (Italy) [presenting]
Abstract: Scalar on function regression models, describing the relationship between a scalar response and a set of $p$ functional predictors, are studied considering the problem of selecting the influential regressors in the presence of outliers. Using a classical basis projection approach, the continuous problem is replaced by a linear discrete one, permitting to adapt the classical penalized M estimators to a grouped problem. In particular the loss functions we will adopt include the Tukeys biweight, the Minimax Concave Penalty (MCP), the penalized Least Absolute Deviation (LAD), the nonnegative garrote, the Welsh and the Cauchy. Numerical implementations of the proposed procedures for proximal like algorithms are discussed. The results are illustrated with simulated examples and a real data analysis.