Outlier Detection for Functional Data Using Principal Components

02/11/2016 - 15:30
02/11/2016 - 16:30
Speaker: 
Matias Salibián-Barrera (University of British Columbia) 2015 CRM-SSC Prize Recipient
Location: 
Salle / Room 6254 (6e étage) Centre de recherches mathématiques Pavillon André-Aisenstadt Université de Montréal 2920, chemin de la Tour
Abstract: 

 Principal components analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate observations. In the functional case, a new characterization of elliptical distributions on separable Hilbert spaces allows us to obtain an equivalent stochastic optimality property for the principal component subspaces of random elements on separable Hilbert spaces. This property holds even when second moments do not exist.

These lower-dimensional approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this talk we propose a new class of robust estimators for principal components, which is consistent for elliptical random vectors, and Fisher-consistent for elliptically distributed random elements on arbitrary Hilbert spaces. We illustrate our method on two real functional data sets, where the robust estimator is able to discover atypical observations in the data that would have been missed otherwise.

Last edited by on Thu, 02/04/2016 - 14:56