{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T07:19:20Z","timestamp":1776755960027,"version":"3.51.2"},"reference-count":36,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"10","license":[{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"Center for Science of Information (CSoI), which is an NSF Science and Technology Center","award":["CCF-0939370"],"award-info":[{"award-number":["CCF-0939370"]}]},{"name":"3Com Stanford Graduate Fellowship"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1109\/tit.2018.2846245","type":"journal-article","created":{"date-parts":[[2018,6,11]],"date-time":"2018-06-11T19:03:50Z","timestamp":1528743830000},"page":"6672-6706","source":"Crossref","is-referenced-by-count":24,"title":["Minimax Estimation of the <inline-formula> \n                     <tex-math notation=\"LaTeX\">$L_{1}$ <\/tex-math>\n                  <\/inline-formula> Distance"],"prefix":"10.1109","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3766-8031","authenticated-orcid":false,"given":"Jiantao","family":"Jiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8335-2364","authenticated-orcid":false,"given":"Yanjun","family":"Han","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tsachy","family":"Weissman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref33","volume":"31","author":"lehmann","year":"1998","journal-title":"Theory of Point Estimation"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1007\/978-88-470-1679-8_10"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2478816"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/BF02401828"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.2307\/2308012"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177011699"},{"key":"ref34","first-page":"5","article-title":"Inequalities on the Lambert W function and hyperpower function","volume":"9","author":"hoorfar","year":"2008","journal-title":"J Inequal Pure Appl Math"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s004409970006"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOS849"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.051139"},{"key":"ref13","author":"wu","year":"2015","journal-title":"Chebyshev polynomials moment matching and optimal estimation of the unseen"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1607774113"},{"key":"ref15","author":"wu","year":"2016","journal-title":"Sample complexity of the distinct elements problem"},{"key":"ref16","author":"han","year":"2016","journal-title":"Minimax rate-optimal estimation of divergences between discrete distributions"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2018.2805844"},{"key":"ref18","first-page":"20","article-title":"Aggregation and high-dimensional statistics","volume":"16","author":"tsybakov","year":"2013","journal-title":"Lecture notes for the course given at the École d'été de Probabilités in Saint-Flour"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s13373-013-0043-1"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2013.01.023"},{"key":"ref4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0711-5","author":"devroye","year":"1996","journal-title":"A Probabilistic Theory of Pattern Recognition"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1963.10500830"},{"key":"ref3","author":"lehmann","year":"2005","journal-title":"Testing Statistical Hypotheses"},{"key":"ref6","first-page":"2157","article-title":"Estimating the unseen: Improved estimators for entropy and other properties","author":"valiant","year":"2013","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref29","author":"tsybakov","year":"2008","journal-title":"Introduction to Nonparametric Estimation"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2011.81"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2548468"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2015.2412945"},{"key":"ref2","author":"cover","year":"2006","journal-title":"Elements of Information Theory"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2620435"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"ref20","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02888-9","volume":"303","author":"devore","year":"1993","journal-title":"Constructive Approximation"},{"key":"ref22","author":"pavlichin","year":"2017","journal-title":"Approximate profile maximum likelihood"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1080\/03610928708829512"},{"key":"ref24","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4778-4","author":"ditzian","year":"1987","journal-title":"Moduli of Smoothness"},{"key":"ref23","first-page":"11","article-title":"A unified maximum likelihood approach for estimating symmetric properties of discrete distributions","author":"acharya","year":"2017","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511813603"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1024404522"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielaam\/18\/8464702\/8379458-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/8464702\/08379458.pdf?arnumber=8379458","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T18:54:35Z","timestamp":1649444075000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8379458\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10]]},"references-count":36,"journal-issue":{"issue":"10"},"URL":"https:\/\/doi.org\/10.1109\/tit.2018.2846245","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10]]}}}