We consider the problem of constructing nonparametric undirected 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 dimension 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
This work has been supported in part by the Collaborative Research Center “Statistical modeling of nonlinear dynamic processes” (SFB 823, Teilprojekt A1,C1) of the German Research Foundation (DFG).
The authors would like to thank Martina Stein who typed parts of this manuscript with considerable technical expertise.
"Nonparametric and high-dimensional functional graphical models." Electron. J. Statist. 16 (2) 6175 - 6231, 2022. https://doi.org/10.1214/22-EJS2087