hal-00178275, version 3
Estimation of Gaussian graphs by model selection
Electronic Journal of Statistics 2 (2008) 542--563
Abstract: 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).
- 1:
- CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
- 2:
- Institut national de la recherche agronomique (INRA) : UR341
- Domain : Mathematics/Statistics
Statistics/Statistics Theory - Keywords : Gaussian Graphical Model – Random matrices – Model selection – Penalized empirical risk – gene regulation networks
- Comment : 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)
- Available versions : v1 (2007-10-10) v2 (2008-04-18) v3 (2008-07-16)
- hal-00178275, version 3
- http://hal.archives-ouvertes.fr/hal-00178275
- oai:hal.archives-ouvertes.fr:hal-00178275
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- Submitted on: Wednesday, 16 July 2008 19:22:27
- Updated on: Wednesday, 16 July 2008 20:29:47
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