Robust Functional Principal Components with sparse observations

BOENTE, GRACIELA; SALIBIAN-BARRERA, MATÍAS; WANG, JANE-LING

Ginebra

Conferencia; International Conference on Robust Statistics (ICORS 2016); 2016

Universidad de Ginebra

In this talk we discuss the problem of robust estimation of functional principal components when only a few observations are available per curve. Manyavailable methods to estimate functional principal components rely on a smoothing step of the observed trajectories, and thus require many observations per curve. A notable exception is the conditional expectation approach of Yao et al. [2005], which estimates the co variance function by smoothing the sparsely available cross-products, and thus is able to combine information from many curves. A first attempt at protecting this approach from potential outliers byusing a robust smoother on the cross-products 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 Xi(t) given Xi(s) as a function of Xi(s) to obtain robust estimators of the scatter function G(t, s) of the underlying random process. Furthermore, this approach allows us to use a robust smoother to combine observations at neighboring points (t, s). In this talk, we report initial numerical experiments comparing the performance of the resulting estimates and existing alternatives.