{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/intrinsic-wavelet-regression-for-surfaces-of","title":"Intrinsic wavelet regression for surfaces of Hermitian positive definite matrices","arxiv_id":"1808.08764","date":"2018-08-27","proceeding":null,"authors":["Joris Chau","Rainer von Sachs"],"abstract":"This paper develops intrinsic wavelet denoising methods for surfaces of Hermitian positive definite matrices, with in mind the application to nonparametric estimation of the time-varying spectral matrix of a multivariate locally stationary time series. First, we construct intrinsic average-interpolating wavelet transforms acting directly on surfaces of Hermitian positive definite matrices in a curved Riemannian manifold with respect to an affine-invariant metric. Second, we derive the wavelet coefficient decay and linear wavelet thresholding convergence rates of intrinsically smooth surfaces of Hermitian positive definite matrices, and investigate practical nonlinear thresholding of wavelet coefficients based on their trace in the context of intrinsic signal plus noise models in the Riemannian manifold. The finite-sample performance of nonlinear tree-structured trace thresholding is assessed by means of simulated data, and the proposed intrinsic wavelet methods are used to estimate the time-varying spectral matrix of a nonstationary multivariate electroencephalography (EEG) time series recorded during an epileptic brain seizure.","url_abs":"http://arxiv.org/abs/1808.08764v1","url_pdf":"http://arxiv.org/pdf/1808.08764v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"intrinsic-wavelet-regression-for-surfaces-of","repo_url":"https://github.com/JorisChau/pdSpecEst","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}