{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:11:46Z","timestamp":1753884706055,"version":"3.41.2"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171016"],"award-info":[{"award-number":["12171016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:p> This paper considers the minimax estimation of the high-dimensional sparse covariance matrices in the presence of missing observations. Based on random missing data, the upper bounds of convergence rate about the data-driven thresholding estimator are constructed over a large class of sparse covariance matrices under the [Formula: see text] norm and the Frobenius norm. In addition, we use Le Cam\u2019s lemma and the relation between the total variation affinity and the Kullback\u2013Leibler divergence to establish the lower bounds which illustrate the desired upper bounds cannot be improved. It is worth mentioning that the approach we adopt to get the lower bounds is simpler than the existing ones. <\/jats:p>","DOI":"10.1142\/s0219691322500217","type":"journal-article","created":{"date-parts":[[2022,5,24]],"date-time":"2022-05-24T10:43:46Z","timestamp":1653389026000},"source":"Crossref","is-referenced-by-count":0,"title":["Minimax optimal estimation of high-dimensional sparse covariance matrices with missing data"],"prefix":"10.1142","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7125-3238","authenticated-orcid":false,"given":"Xinyu","family":"Qi","sequence":"first","affiliation":[{"name":"College of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8175-133X","authenticated-orcid":false,"given":"Jinru","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaochen","family":"Zeng","sequence":"additional","affiliation":[{"name":"College of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,7,7]]},"reference":[{"doi-asserted-by":"publisher","key":"S0219691322500217BIB001","DOI":"10.1214\/009053606000000074"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB002","DOI":"10.1093\/biomet\/asy011"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB003","DOI":"10.1214\/009053607000000758"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB004","DOI":"10.1214\/08-AOS600"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB005","DOI":"10.1214\/12-AOS999"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB006","DOI":"10.1016\/j.jmva.2016.05.002"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB007","DOI":"10.1214\/09-AOS752"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB008","DOI":"10.1214\/12-AOS998"},{"key":"S0219691322500217BIB009","first-page":"1319","volume":"22","author":"Cai T. T.","year":"2012","journal-title":"Statist. Sinica"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB010","DOI":"10.1214\/09-AOS720"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB011","DOI":"10.1007\/b13794"},{"doi-asserted-by":"publisher","key":"S0219691322500217BIB012","DOI":"10.1007\/978-1-4612-1880-7_29"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691322500217","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T02:01:03Z","timestamp":1664157663000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691322500217"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,7]]},"references-count":12,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["10.1142\/S0219691322500217"],"URL":"https:\/\/doi.org\/10.1142\/s0219691322500217","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2022,7,7]]},"article-number":"2250021"}}