A Wavelet-Based Independence Test for Functional Data with an Application to MEG Functional Connectivity

[2009.11452] A Wavelet-Based Independence Test for Functional Data with an Application to MEG Functional Connectivity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Methodology arXiv:2009.11452 (stat) [Submitted on 24 Sep 2020 ( v1 ), last revised 16 Aug 2026 (this version, v2)] Title: A Wavelet-Based Independence Test for Functional Data with an Application to MEG Functional Connectivity Authors: Rui Miao , Xiaoke Zhang , Raymond K. W. Wong View a PDF of the paper titled A Wavelet-Based Independence Test for Functional Data with an Application to MEG Functional Connectivity, by Rui Miao and 2 other authors View PDF HTML (experimental) Abstract: Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification, while a model-free method only provides a correlation measure which is inadequate to test independence. In this paper, we adopt the Hilbert-Schmidt Independence Criterion (HSIC) to measure the dependency between two random functions. We develop a two-step procedure by first pre-smoothing each function based on its discrete and noisy measurements and then applying the HSIC to recovered functions. To ensure the compatibility between the two steps such that the effect of the pre-smoothing error on the subsequent HSIC is asymptotically negligible when the data are densely measured, we propose a new wavelet thresholding method for pre-smoothing and to use Besov-norm-induced kernels for HSIC. We also provide the corresponding asymptotic analysis. The superior numerical performance of the proposed method over existing ones is demonstrated in a simulation study. Moreover, in an magnetoencephalography (MEG) data application, the functional connectivity patterns identified by the proposed method are more anatomically interpretable than those by existing methods. Subjects: Methodology (stat.ME) ; Applications (stat.AP) Cite as: arXiv:2009.11452 [stat.ME] (or arXiv:2009.11452v2 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2009.11452 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Rui Miao [ view email ] [v1] Thu, 24 Sep 2020 02:21:37 UTC (16,431 KB) [v2] Sun, 16 Aug 2026 00:24:30 UTC (10,698 KB) Full-text links: Access Paper: View a PDF of the paper titled A Wavelet-Based Independence Test for Functional Data with an Application to MEG Functional Connectivity, by Rui Miao and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2020-09 Change to browse by: stat stat.AP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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