{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T13:37:11Z","timestamp":1791207431257,"version":"4.1.0"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>\n                    In this paper, we improve known results on the convergence rates of spectral distributions of large-dimensional sample covariance matrices of size p \u00d7 n. Using the Stieltjes transform, we first prove that the expected spectral distribution converges to the limiting Marcenko--Pastur distribution with the dimension sample size ratio y=y\n                    <jats:sub>n<\/jats:sub>\n                    =p\/n at a rate of O(n\n                    <jats:sup>- 1\/2<\/jats:sup>\n                    ) if y keeps away from 0 and 1, under the assumption that the entries have a finite eighth moment. Furthermore, the rates for both the convergence in probability and the almost sure convergence are shown to be O\n                    <jats:sub>p<\/jats:sub>\n                    (n\n                    <jats:sup>-2\/5<\/jats:sup>\n                    ) and o\n                    <jats:sub>a.s.<\/jats:sub>\n                    (n\n                    <jats:sup>-2\/5+\\eta<\/jats:sup>\n                    ), respectively, when y is away from 1. It is interesting that the rate in all senses is O(n\n                    <jats:sup>-1\/8<\/jats:sup>\n                    ) when y is close to 1.\n                  <\/jats:p>","DOI":"10.1137\/s0895479801385116","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"105-127","source":"Crossref","is-referenced-by-count":30,"title":["Convergence Rates of Spectral Distributions of Large Sample Covariance Matrices"],"prefix":"10.1137","volume":"25","author":[{"given":"Z. D.","family":"Bai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baiqi","family":"Miao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian-feng","family":"Yao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176989261"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176989262"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1024404298"},{"key":"R4","first-page":"611","volume":"9","author":"Bai Z.","year":"1999","journal-title":"Statist. 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(N.S.)"},{"key":"R14","volume-title":"Random matrices","author":"Mehta Madan","year":"1991"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/0516047"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.2307\/1970079"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.2307\/1970008"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00353874"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479801385116","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:40:57Z","timestamp":1787334057000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479801385116"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479801385116"],"URL":"https:\/\/doi.org\/10.1137\/s0895479801385116","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}