Nonparametric and high-dimensional functional graphical models

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 vertices or linear conditional means. In article, we provide more flexible model which relaxes linearity assumption by replacing it an arbitrary additive form. The use principal components offers estimation strategy that uses group lasso penalty to estimate relevant edges graph. establish guarantees resulting estimators, can be used prove consistency if dimension and number diverge infinity with sample size. also investigate empirical performance our method through simulation studies real data application