A Novel Approach To Estimate Functional Gaussian Graphical Model Based On Penalized Multivariate FunctionalRegression Model

Abstract

In this article we contribute to the literature on the functional Gaussian graphical model by introducing a new penalty function for the multivariate functional regression model that allows us to have a direct connection between the estimated parameters and conditional dependencies among the functional curves, i.e.the edge set of the graphical model. Introducing the model in infinite dimensional space, we show how to estimate the model in a finite-dimensional subspace. A focus is also given on how the bases and scores for the Karhunen-Loéve expansion of the curves are obtained. The performance of the proposed method is evaluated by a simulation study and compared with that of other better-known models in the literature, showing good performance.