Nonparametric Functional Graphical Modeling through Functional Additive Regression Operator

In this article, we develop a nonparametric graphical model for multivariate random functions. Most existing models are restricted by the assumptions of Gaussian or copula distributions, which also imply linear relations among variables functions on different nodes. We relax those building our based new statistical object—the functional additive regression operator. By carrying out and neighborhood selection at operator level, method can capture nonlinear without requiring any distributional assumptions. Moreover, is built up using only one-dimensional kernel, thus, avoids curse dimensionality from fully approach often suffers, enables us to work with large-scale networks. derive error bounds estimated establish graph estimation consistency, while allowing number diverge exponential rate sample size. demonstrate efficacy both simulations analysis an electroencephalography dataset. Supplementary materials article available online.