Nonparametric and high-dimensional functional graphical models
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Date
2021
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Abstract
We consider the problem of constructing nonparametric undirected graphical models for highdimensional
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.
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Keywords
undirected graphical models, brain networks, EEG data, lasso, additive models, functional data