A Gaussian graphical model is a statistical model, where the data follows a multivariate Normal distribution in which conditional independence relations of the random vector are encoded in a graph. Testing the hypothesis that a Gaussian graphical model is associated to either a graph or a specific subgraph corresponds to a composite hypothesis test in the Normal model. However, the standard likelihood ratio test for this problem has both poor power and size, and is only suitable if the sample size is large compared to the number of observations. In this thesis, we review higher-order approximations methods and apply them to subgraph testing in Gaussian graphical models. This allows us to define a transformation of the likelihood ratio statistic for which an accurate finite-sample distributional approximation is available. A simulation study shows that in settings of small and large sample sizes, the introduced statistical test is robust and favorable to the likelihood ratio test in terms of both power and size.     «

A Gaussian graphical model is a statistical model, where the data follows a multivariate Normal distribution in which conditional independence relations of the random vector are encoded in a graph. Testing the hypothesis that a Gaussian graphical model is associated to either a graph or a specific subgraph corresponds to a composite hypothesis test in the Normal model. However, the standard likelihood ratio test for this problem has both poor power and size, and is only suitable if the sample siz...     »