Open Access
2022 Nonparametric and high-dimensional functional graphical models
Eftychia Solea, Holger Dette
Author Affiliations +
Electron. J. Statist. 16(2): 6175-6231 (2022). DOI: 10.1214/22-EJS2087


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

Funding Statement

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.


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Eftychia Solea. Holger Dette. "Nonparametric and high-dimensional functional graphical models." Electron. J. Statist. 16 (2) 6175 - 6231, 2022.


Received: 1 October 2021; Published: 2022
First available in Project Euclid: 22 November 2022

arXiv: 2103.10568
MathSciNet: MR4515718
zbMATH: 07633936
Digital Object Identifier: 10.1214/22-EJS2087

Primary: 60K35 , 60K35
Secondary: 60K35

Keywords: Additive models , Conditional independence , functional data , Lasso , undirected graphical models

Vol.16 • No. 2 • 2022
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