{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:24:53Z","timestamp":1753881893381,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/100007847","name":"Natural Science Foundation of Jilin Province","doi-asserted-by":"publisher","award":["12171016"],"award-info":[{"award-number":["12171016"]}],"id":[{"id":"10.13039\/100007847","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":[[2023,7]]},"abstract":"<jats:p> Motivated by Jin\u2013Ke\u2013Wang\u2019s work (J. Jin, Z. T. Ke and W. Wang, Ann. Statist.\u00a045(5) (2017) 2151\u20132189), this paper studies estimation of misclassification rate in the Asymptotic Rare and Weak (ARW) model. In contrast to Jin\u2013Ke\u2013Wang\u2019s theorem, we measure the performance of the estimator by the misclassification rate instead of Hamming distance, and extend the Gaussian noise to sub-Gaussian\u2019s. The probability estimation with convergence rate is first given under some conditions. Then we prove that condition necessary as well. A direct corollary of our estimation can be compared with Jin\u2013Ke\u2013Wang\u2019s theorem. It turns out that our statistical limit coincides with theirs. <\/jats:p>","DOI":"10.1142\/s0219691323500017","type":"journal-article","created":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T09:31:28Z","timestamp":1671701488000},"source":"Crossref","is-referenced-by-count":0,"title":["Estimation of misclassification rate in the Asymptotic Rare and Weak model with sub-Gaussian noises"],"prefix":"10.1142","volume":"21","author":[{"given":"Youming","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9575-2162","authenticated-orcid":false,"given":"Zhentao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,1,12]]},"reference":[{"issue":"1","key":"S0219691323500017BIB002","first-page":"60","volume":"46","author":"Cai T. T.","year":"2018","journal-title":"Ann. Statist."},{"issue":"3","key":"S0219691323500017BIB005","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1214\/009053604000000265","volume":"32","author":"Donoho D.","year":"2004","journal-title":"Ann. Statist."},{"issue":"5","key":"S0219691323500017BIB006","first-page":"2074","volume":"45","author":"Gao C.","year":"2017","journal-title":"Ann. Statist."},{"issue":"5","key":"S0219691323500017BIB007","first-page":"2151","volume":"45","author":"Jin J.","year":"2017","journal-title":"Ann. Statist."},{"volume-title":"Concentration Inequalities and Model Selection","year":"2007","author":"Massart P.","key":"S0219691323500017BIB010"},{"volume-title":"Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis","year":"2017","author":"Mitzenmacher M.","key":"S0219691323500017BIB011"},{"key":"S0219691323500017BIB013","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1017\/CBO9780511794308.006","volume-title":"Compressed Sensing, Theory and Applications","author":"Vershynin R.","year":"2012"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691323500017","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T08:39:59Z","timestamp":1688373599000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691323500017"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,12]]},"references-count":7,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["10.1142\/S0219691323500017"],"URL":"https:\/\/doi.org\/10.1142\/s0219691323500017","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2023,1,12]]},"article-number":"2350001"}}