Estimation of Gaussian graphs by model selection

Details Estimation of Gaussian graphs by model selection Estimation of Gaussian graphs by model selection

2007-10-10

arxiv.org/abs/0710.2044v3

Electronic Journal of Statistics 2 (2008) 542--563

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-EJS228 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/08-EJS228

We 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).

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