Title: Nonparametric graphical models for high-dimensional functional data
Authors: Eftychia Solea - Ruhr Universität Bochum (Germany) [presenting]
Holger Dette - Ruhr-Universitaet Bochum (Germany)
Abstract: We consider the problem of constructing nonparametric undirected graphical models for multivariate functional data. Most existing approaches on graphical models assume either the Gaussian distribution on the vertices or linear conditional means. The presented approach provides a more flexible model which relaxes the linearity assumption by replacing it by an arbitrary additive form. The utilisation of the functional principal components offers an estimation strategy that uses a group lasso penalty to estimate the relevant edges of the graph. We establish the model selection consistency for the resulting estimator, while allowing both the number of predictors and the number of functional principal components to diverge to infinity with the sample size. We investigate the empirical performance of our method through simulation studies and a real data application.