Tests for Gaussian graphical models
Résumé
Gaussian graphical models are promising tools for analysing genetic networks. However, assessing a network using microarray experiments arises difficult statistical and computational questions. In the present paper, we construct a procedure for testing the neighborhoods of a Gaussian graphical model. Our approach is based on the connection between local Markov property and conditional regression of a Gaussian random variable. Thus, we adapt the testing procedures defined in a preceding paper (N. Verzelen and F.Villers, Goodness-of-fit Tests for high-dimensional Gaussian linear models, Arxiv:math.ST/0711.2119) to this Gaussian graphical modelling framework. Our new tests then inherits appealing theoretical properties. Besides, they apply and are computationally feasible in a high-dimensional setting: the number of observations may be much smaller than the number of nodes. A large part of this study is deserved to illustrate and discuss the application of our procedures to simulated data and to biological data.
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