Elliptical distributions and outlier detection for functional data

BOENTE, GRACIELA; SALIBIAN-BARRERA, MATÍAS; TYLER, DAVID

Londres

Conferencia; VIII International Conference of the ERCIM Working Group on Computing & Statistics (ERCIM2015).; 2015

Imperial College, Birkbeck University,Queen Mary University of London, Royal Statistical Society

As in the multivariate setting, the class of elliptical distributions on separable Hilbert spaces serves as an important vehicle and reference point for the development and evaluation of robust methods in functional data analysis. For example, they allow us to study the Fisher-consistencyof robust estimators for functional data when second moments may notexist. We present a simple characterization of elliptical distributions on separable Hilbert spaces that allows us to establish a stochastic optimality property for the principal component subspaces associated with elliptically distributed random elements, without requiring finite second moments. These lower-dimensional approximations can be very useful in identifyingpotential outliers among functional observations, and we present a robust estimator for the principal subspaces. We illustrate our method on real functional data sets, where the robust estimator is able to discover atypical observations in the data that would have been missed otherwise. Through a simulation study, we also study its performance when used to detect outlying observations.