Estimation of Gaussian graphs by model selection

Christophe Giraud (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

Our aim in this paper is to investigate Gaussian graph estimation from a theoretical and non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and we focus on the disadvantageous case where n is smaller than p. To estimate the graph of conditional dependences of P_C, we propose to introduce a collection of candidate graphs and then select one of them by minimizing a penalized empirical risk. Our main result assess the performance of the procedure in a non-asymptotic setting. We pay a special attention to the maximal degree D of the graphs that we can handle, which turns to be roughly n/(2log p).

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

Christophe Giraud. Estimation of Gaussian graphs by model selection. 2007. ⟨hal-00180837⟩