Abstract
In this paper, we develop tools for statistical inference on replicated realizations of spatiotemporal processes that are locally time-harmonizable. Our method estimates both the rescaled spatial time-varying Loève-spectrum and the spatial time-varying dual-frequency coherence function under realistic modeling assumptions. We construct confidence intervals for these parameters of interest using the Circular Block Bootstrap method and prove its consistency. We illustrate the application of our methodology on a dataset arising from an experiment in neuropsychology. From EEG recordings, our method allows studying the dynamic functional connectivity within the brain associated to visual working memory performance.
Funding Statement
Anna Dudek acknowledges support from the King Abdullah University of Science and Technology (KAUST) Research Grant OSR-2019-CRG8-4057.2. Denes Szucs and Lincoln Colling are funded by James S. McDonnell Foundation 21st Century Science Initiative in Understanding Human Cognition (grant number 220020370; received by Denes Szucs).
Acknowledgments
We thank the editor and the anonymous reviewers for their comments, which helped us to improve the manuscript.
Citation
John Aston. Dominique Dehay. Anna E. Dudek. Jean-Marc Freyermuth. Denes Szucs. Lincoln Colling. "Spectrum inference for replicated spatial locally time-harmonizable time series." Electron. J. Statist. 17 (1) 1371 - 1410, 2023. https://doi.org/10.1214/23-EJS2130
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