Gaussian stationary processes over graphs, general frame and maximum likelihood identification

Thibault Espinasse (1) , Fabrice Gamboa (1) , Jean-Michel Loubes (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we give a general construction of stationary Gaussian processes indexed on graphs. This construction relies on spectral theory of Hilbertian operators defined on a graph. We then extend natural maximum likelihood estimators of the parameters of the corresponding spectral density and provide their asymptotic behaviour.

Mots clés: Stochastic processes; Graphs; Graphical Models; Gaussian fields

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Thibault Espinasse, Fabrice Gamboa, Jean-Michel Loubes. Gaussian stationary processes over graphs, general frame and maximum likelihood identification. 2011. ⟨hal-00586905v2⟩