AI & ML
High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series
arXiv stat.TH0 views
arXiv:2609.30565v2 Announce Type: replace-cross Abstract: Many real-world high-dimensional time series exhibit long-memory, but Gaussian graphical model testing in this regime remains understudied. We develop a direct, data-adaptive test statistic for assessing conditional independence in the graph structure of stationary Gaussian time series. We establish a finite-sample, Berry--Esseen type Gaussian approximation bound for the statistic, which applies to both short-memory and long-memory time series. The testing procedure uses a block bootstrap method, on which we provide a finite-sample validity result including in the ultra-high-dimensional scenario, and can be extended to comparing graphical structures in two-sample tests. We also develop a consistency-empowered correction to the statistic and show that such tests attain asymptotic consistency in both size and power. Our proposed method is applied to real-world fMRI data to understand functional connectivities within brain in different periods.
Source：https://arxiv.org/abs/2609.30565PreviousCounterexamples and Sufficient Conditions: Comments on "Optimally-Transported Generalized Method of Moments"NextDecentralized Sparse Quantile Regression
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