B0805
Title: Adaptive functional principal components analysis
Authors: Sunny Wang - ENSAI (France) [presenting]
Valentin Patilea - CREST-Ensai (France)
Abstract: Kernel estimators are built for the mean and the covariance functions of functional data, and they are used for functional PCA. The random trajectories are, not necessarily differentiable, have unknown, possibly non-constant regularity, and are measured with possibly heteroscedastic error, at discrete design points. We propose specific bandwidth rules for the eigenvalues and the eigenfunctions, respectively. The bandwidth adapts to the local regularity of the trajectories, and minimises the mean squared error between our eigenelements' estimates and the ideal ones, which would be obtained if the curves were observed in continuous time, without noise. They can be applied with both sparsely or densely sampled curves, are easy to calculate and update, and perform well in simulations. Simulations illustrate the effectiveness of the new approach.
