2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164896We investigate in this paper the estimation of Gaussian graphs by model selection from a non-asymptotic point of view. We start from a n-sample of a Gaussian law P_C in R^p and focus on the disadvantageous case where n is smaller than p. To estimate the graph of conditional dependences of P_C, we 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/(2 log p).Published in at http://dx.doi.org/10.1214/08-EJS228 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62G08 (Primary) 15A52, 62J05 (Secondary)text