Nonparametric and high-dimensional functional graphical models

We consider the problem of constructing nonparametric undi-rected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear conditional means. In this article, we provide a more flexible model which relaxes the linearity assumption by replacing it by an arbitrary additive form. The use of functional principal components offers an estimation strategy that uses a group lasso penalty to estimate the relevant edges of the graph. We establish statistical guarantees for the resulting estimators, which can be used to prove consistency if the dimen-sion and the number of functional principal components diverge to infinity with the sample size. We also investigate the empirical performance of our method through simulation studies and a real data application

Automated summary

This article focuses on constructing nonparametric undirected graphical models for high-dimensional functional data. A more flexible model is proposed, replacing the linearity assumption with an arbitrary additive form. The use of functional principal components and a group lasso penalty allows for estimation of the relevant edges of the graph. Statistical guarantees are established, and empirical performance is evaluated through simulation studies and a real data application.