{"title":"Convergence presque sûre de l'estimateur linéaire local de la fonction de répartition conditionnelle","authors":"Gilles R. Ducharme, Mariem Mint El Mouvid","doi":"10.1016/S0764-4442(01)02113-9","DOIUrl":null,"url":null,"abstract":"<div><p>The local linear estimator of the conditional cumulative distribution function is shown to be the ratio of two <em>U</em>-statistics. Using results from the theory of <em>U</em>-statistics, we show the almost sure convergence of this estimator both locally and globally. This is used to establish the almost sure convergence of conditional quantiles computed from the linear estimator.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 873-876"},"PeriodicalIF":0.0000,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02113-9","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
The local linear estimator of the conditional cumulative distribution function is shown to be the ratio of two U-statistics. Using results from the theory of U-statistics, we show the almost sure convergence of this estimator both locally and globally. This is used to establish the almost sure convergence of conditional quantiles computed from the linear estimator.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
