Robust estimators under a functional common principal components model

BALI, JUAN LUCAS; BOENTE, GRACIELA

Oviedo

Conferencia; Fifth International Conference of the ERCIM Working Group on Computing & Statistics; 2012

European Research Consortium for Informatics and Mathematics, International Association for Statistical Computing, Universidad de Oviedo, Queen Mary University of London

When dealing with several populations of functional data, equality of the covariance operators is often assumed. Usually, if this assumption does not hold, one estimates the covariance operator of each group separately, which leads to a large number of parameters. As in the multivariate setting,this is not satisfactory since the covariance operators may exhibit some common structure. We discuss the extension to the functional setting of projection-pursuit estimators for the common directions under a common principal component model that has been widely studied when dealing with multivariate observations. We present estimators of the unknown parameters combining robust projection?pursuit with different smoothing methods. We obtain consistency results under mild assumptions.