Electronic Journal of Statistics

Estimation of Gaussian graphs by model selection

Christophe Giraud

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

Article information

Electron. J. Statist., Volume 2 (2008), 542-563.

First available in Project Euclid: 16 July 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 15A52 62J05: Linear regression

Gaussian graphical model Random matrices Model selection Penalized empirical risk


Giraud, Christophe. Estimation of Gaussian graphs by model selection. Electron. J. Statist. 2 (2008), 542--563. doi:10.1214/08-EJS228. https://projecteuclid.org/euclid.ejs/1216238023

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