{"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/estimation-of-large-covariance-and-precision","title":"Estimation of Large Covariance and Precision Matrices from Temporally Dependent Observations","arxiv_id":"1412.5059","date":"2014-12-16","proceeding":null,"authors":["Hai Shu","Bin Nan"],"abstract":"We consider the estimation of large covariance and precision matrices from\nhigh-dimensional sub-Gaussian or heavier-tailed observations with slowly\ndecaying temporal dependence. The temporal dependence is allowed to be\nlong-range so with longer memory than those considered in the current\nliterature. We show that several commonly used methods for independent\nobservations can be applied to the temporally dependent data. In particular,\nthe rates of convergence are obtained for the generalized thresholding\nestimation of covariance and correlation matrices, and for the constrained\n$\\ell_1$ minimization and the $\\ell_1$ penalized likelihood estimation of\nprecision matrix. Properties of sparsistency and sign-consistency are also\nestablished. A gap-block cross-validation method is proposed for the tuning\nparameter selection, which performs well in simulations. As a motivating\nexample, we study the brain functional connectivity using resting-state fMRI\ntime series data with long-range temporal dependence.","url_abs":"http://arxiv.org/abs/1412.5059v5","url_pdf":"http://arxiv.org/pdf/1412.5059v5.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":"abstracts"},"code_links":[{"paper_slug":"estimation-of-large-covariance-and-precision","repo_url":"https://github.com/shu-hai/SpatialCOVforTimeSeries","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":null,"task_name":"Functional Connectivity"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}