Robust functional principal components: a projection-pursuit approach

Professor David E. Tyler from Rutgers University will give a talk on "Robust functional principal components: a projection-pursuit approach".

Abstract

In many situations, data are not simply univariate or multivariate observations, but rather a data point may be a function itself, e.g., data which is recorded over a period of time. The statistical study of such data is commonly referred to as functional data analysis.

Functional data analysis methods are typically extensions of multivariate methods, such as principal components analysis. As with multivariate data, it is possible to have hidden outliers in functional data and so there is a need for robust methods in this area. The literature on robust methods and in particular robust principal components in the functional data setting though is rather sparse.

In this talk, the difficulty of extending robust multivariate principal components analysis to the functional data setting is first discussed. It is then noted that one promising robust method which can be extended is the projection pursuit approach to robust principal component analysis. This approach for functional data, together with different smoothing methods, is presented and studied. Consistency results are shown under mild assumptions. The performance of the classical and robust procedures are compared via a simulation study under different contamination schemes.

This work is joint with Luca Bali and Graciela Boente of the University of Buenos Aires and with Jane-Ling Wang of UCDavis.