Outlier Detection for Functional Data Using Principal Components

• Activity Number: 383
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Matias Salibian*+ and Graciela Boente
• Companies: University of British Columbia and Universidad de Buenos Aires
• Keywords: Robustness ; Functional Data ; Principal Components ; Outlier detection

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 and simple characterization of elliptical distributions on separable Hilbert spaces allows us to obtain an equivalent stochastic optimality property for the principal component subspaces associated with elliptically distributed random elements. 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. Our method is consistent for elliptical random vectors, and is Fisher-consistent for elliptically distributed random elements on arbitrary Hilbert spaces. We illustrate 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.

This talk is the result of recent collaborations with Graciela Boente and David Tyler.