{"title":"条件分布函数的局部线性估计量几乎肯定收敛","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":"{\"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}","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}
Convergence presque sûre de l'estimateur linéaire local de la fonction de répartition conditionnelle
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.
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