{"title":"自归一化极限定理综述","authors":"Q. Shao, Qiying Wang","doi":"10.1214/13-PS216","DOIUrl":null,"url":null,"abstract":"ni=1 Xi and V 2 n = P n i=1 X 2 i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum Sn/Vn. Other self-normalized limit theorems are also briefly discussed. MSC 2010 subject classifications: Primary 60F05, 60F17; secondary 62E20.","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":"10 1","pages":"69-93"},"PeriodicalIF":1.3000,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/13-PS216","citationCount":"41","resultStr":"{\"title\":\"Self-normalized limit theorems: A survey\",\"authors\":\"Q. Shao, Qiying Wang\",\"doi\":\"10.1214/13-PS216\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"ni=1 Xi and V 2 n = P n i=1 X 2 i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum Sn/Vn. Other self-normalized limit theorems are also briefly discussed. MSC 2010 subject classifications: Primary 60F05, 60F17; secondary 62E20.\",\"PeriodicalId\":46216,\"journal\":{\"name\":\"Probability Surveys\",\"volume\":\"10 1\",\"pages\":\"69-93\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2013-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1214/13-PS216\",\"citationCount\":\"41\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Surveys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/13-PS216\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Surveys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/13-PS216","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
ni=1 Xi and V 2 n = P n i=1 X 2 i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum Sn/Vn. Other self-normalized limit theorems are also briefly discussed. MSC 2010 subject classifications: Primary 60F05, 60F17; secondary 62E20.
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