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2008 Estimation of Gaussian graphs by model selection
Christophe Giraud
Electron. J. Statist. 2: 542-563 (2008). DOI: 10.1214/08-EJS228

Abstract

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).

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Christophe Giraud. "Estimation of Gaussian graphs by model selection." Electron. J. Statist. 2 542 - 563, 2008. https://doi.org/10.1214/08-EJS228

Information

Published: 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1320.62094
MathSciNet: MR2417393
Digital Object Identifier: 10.1214/08-EJS228

Subjects:
Primary: 62G08
Secondary: 15A52 , 62J05

Keywords: Gaussian graphical model , Model selection , Penalized empirical risk , random matrices

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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