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Titel
Nonparametric and high-dimensional functional graphical models / Eftychia Solea, Holger Dette
Weitere Titel
Nonparametric and highdimensional functional graphical models
VerfasserSolea, Eftychia ; Dette, Holger
Erschienen[Dortmund] : SFB 823, 2021
Ausgabe
Elektronische Ressource
Umfang1 Online-Ressource (52 Seiten) : Diagramme
SerieDiscussion paper ; Nr. 9 (2021)
SchlagwörterStatistik / Nichtparametrisches Modell
URNurn:nbn:de:hbz:6:2-1472971 
DOI10.17877/DE290R-21978 
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Nonparametric and high-dimensional functional graphical models [0.85 mb]
Zusammenfassung

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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Statistik
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