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We study high-dimensional graphical models for non-Gaussian functional data. To relax the Gaussian assumption, we consider the functional Gaussian copula graphical model proposed by Solea and Li [Copula Gaussian graphical models for functional data. J Am Stat Assoc. 2022;117(538):781–793]. To estimate robustly the conditional independence relationships among the functions, we propose a new rank-based correlation operator, the Kendall's tau correlation operator that extends the Kendall's tau correlation matrix at the functional setting. We establish new concentration inequalities and bounds of the rank-based estimator, which guarantee graph estimation consistency. We consider both completely and partially observed functional data, while allowing the graph size to grow with the sample size and accounting for the errors in the estimated functional principal components scores. We illustrate the finite sample properties of our method through simulation studies and a brain data set collected from functional magnetic resonance imaging for ADHD subjects.

High-dimensional rank-based graphical models for non-Gaussian functional data