Robust inference in functional data analysis using S-estimators

BOENTE, GRACIELA; SALIBIAN-BARRERA, MATÍAS

Stresa

Workshop; IWFOS 2014 (Third International Workshop on Functional and Operatorial Statistics); 2014

Universita del Piemonte Orientale, Institut de Mathématiques de Toulouse, Dipartimento di Matematica, Politecnico di Milano

Principal components analysis attempts to find a lower dimensional representation of the data that retains as much information as possible. For functional data, this means looking for the best q-dimensional approximation to a random element over a separable Hilbert space. In this note we discuss the problem of robustly estimating these finite-dimensional approximating linear subspaces using robust scale estimators. In analogy to the linear regression case, we refer to these estimators as S-estimators.