{"title":"期望Wasserstein距离中经验测度的收敛性:Rd中的非渐近显式界","authors":"N. Fournier","doi":"10.1051/ps/2023011","DOIUrl":null,"url":null,"abstract":"Abstract. We provide some non asymptotic bounds, with explicit constants, that measure the rate of convergence, in expected Wasserstein distance, of the empirical measure associated to an i.i.d. N -sample of a given probability distribution on R d .","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"76 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in Rd\",\"authors\":\"N. Fournier\",\"doi\":\"10.1051/ps/2023011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. We provide some non asymptotic bounds, with explicit constants, that measure the rate of convergence, in expected Wasserstein distance, of the empirical measure associated to an i.i.d. N -sample of a given probability distribution on R d .\",\"PeriodicalId\":51249,\"journal\":{\"name\":\"Esaim-Probability and Statistics\",\"volume\":\"76 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/ps/2023011\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/ps/2023011","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Convergence of the empirical measure in expected Wasserstein distance: non asymptotic explicit bounds in Rd
Abstract. We provide some non asymptotic bounds, with explicit constants, that measure the rate of convergence, in expected Wasserstein distance, of the empirical measure associated to an i.i.d. N -sample of a given probability distribution on R d .
期刊介绍：
The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains.
Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics.
Long papers are very welcome.
Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.
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