Robust methods for functional principal components

BALI, JUAN LUCAS; BOENTE, GRACIELA; TYLER, DAVID; WANG, JANE-LING

Limassol

Workshop; Second Workshop of the ERCIM Working Group on Computing & Statistics; 2009

European Research Consortium for Informatics and Mathematics, International Association for Statistical Computing.

When dealing with multivariate data, like classical PCA, robust PCA searches for directions with maximal dispersion of the data projected on it. Instead of using the variance as a measure of dispersion, a robust scale estimator can be used in the maximization problem in order to get robust estimators. The aim is to adapt the projection pursuit approach to the functional setting and to study the asymptotic behavior of the proposals. Sometimes instead of raw robust functional principal component estimators, smoothed ones can be of interest. We will discuss three approaches to obtain smoothed estimators. Two of them are based on penalizing either the norm or the robust scale function. The third one is related to B-splines and sieve estimation. Through a simulation study, the performance of the different proposals with the classical ones is compared under a Gaussian distribution and different contamination schemes.