On robust functional principal components

BOENTE, GRACIELA; SALIBIAN-BARRERA, MATÍAS

Valladolid

Conferencia; International Conference on Robust Statistics (ICORS 2011); 2011

We study robust estimates of principal components for functional data. Since in general principal components can be shown to give the best finitedimensional approximation to random elements over separable Hilbert spaces, we consider the problem of robustly estimating these finite-dimensional approximating subspaces. We obtain some general optimality results and study the properties of previously proposed estimators that can be used in this setting. Finally, we discuss a new family of estimators that we call S-estimators. This work is motivated by a problem of outlier detection in atmospheric data collected by weather balloons launched into the amosphere and stratosphere.