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Abstract:
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There has been considerable interest in estimating and testing for conditional dependence relationships among random variables in the high-dimensional setting. Time-varying Gaussian graphical models is an important class of graphical models to model conditional dependence relationships that evolve over time. In this paper, we propose an inferential framework to test the topological structure of a time-varying graph. Our inferential framework includes but are not limited to testing the number of connected components and maximum degree of a time-varying graph. As a special case, our testing procedure can also be used for testing the topological structure of a single graphical model. We establish the validity of the proposed testing procedure by showing that the Type I error can be controlled at a pre-specified level. We show using simulation studies that our proposal is able to control the Type I error and that the power of the proposed procedure increases to one as we increase the sample size. Finally, we apply our proposed method to infer the topological structure of a brain connectivity network using a functional magnetic resonance imaging dataset.
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