A0174
Title: Robust functional principal components with sparse observations
Authors: Matias Salibian-Barrera - The University of British Columbia (Canada) [presenting]
Graciela Boente - Universidad de Buenos Aires (Argentina)
Jane-Ling Wang - University of California Davis (United States)
Abstract: Principal components analysis provides an optimal lower-dimensional approximation to multivariate observations. Similarly, functional principal components analysis may yield parsimonious predictions for each trajectory in the sample. A new characterization of elliptical distributions on separable Hilbert spaces shows that this holds even when second moments do not exist. We discuss the problem of robust estimation of functional principal components when only a few observations are available per curve. The conditional expectation approach estimates the covariance function by smoothing the sparsely available cross-products, and thus ``combines information'' from many sparse curves. A first attempt at protecting this approach from outliers by using a robust smoother does not work because the distribution of the cross-products is generally asymmetric. However, when the stochastic process has an elliptical distribution, one can exploit the linear structure of the conditional distribution of the process at time $t$ conditional on its value at time s to obtain robust estimators of the scatter function $G(t,s)$.
