{"title":"隐藏马尔可夫模型的普遍一致条件u统计量","authors":"Michel Harel , Madan L Puri","doi":"10.1016/S0764-4442(01)02148-6","DOIUrl":null,"url":null,"abstract":"<div><p>A general class of conditional <em>U</em>-statistics was introduced by W. Stute [3] as a generalization of the Nadaraya–Watson estimates of a regression function. It was shown that such statistics are universally consistent (Stute [3]). Also, universal consistency of the window and <em>k</em><sub><em>n</em></sub>-nearest neighbor estimators (as two special cases of the conditional <em>U</em>-statistics) were proved by Stute [3]. In this paper, we extend these results from the independent case to dependent case.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 10","pages":"Pages 953-956"},"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)02148-6","citationCount":"2","resultStr":"{\"title\":\"U-statistiques conditionnelles universellement consistantes pour des modèles de Markov cachés\",\"authors\":\"Michel Harel , Madan L Puri\",\"doi\":\"10.1016/S0764-4442(01)02148-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A general class of conditional <em>U</em>-statistics was introduced by W. Stute [3] as a generalization of the Nadaraya–Watson estimates of a regression function. It was shown that such statistics are universally consistent (Stute [3]). Also, universal consistency of the window and <em>k</em><sub><em>n</em></sub>-nearest neighbor estimators (as two special cases of the conditional <em>U</em>-statistics) were proved by Stute [3]. In this paper, we extend these results from the independent case to dependent case.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 10\",\"pages\":\"Pages 953-956\"},\"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)02148-6\",\"citationCount\":\"2\",\"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/S0764444201021486\",\"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/S0764444201021486","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
摘要
W. Stute[3]引入了一类一般的条件u统计量，作为回归函数的Nadaraya-Watson估计的推广。研究表明，这些统计数据是普遍一致的(Stute[3])。此外，Stute[3]证明了窗口估计量和k近邻估计量(作为条件u统计量的两种特殊情况)的普遍一致性。在本文中，我们将这些结果从独立情况推广到相关情况。
U-statistiques conditionnelles universellement consistantes pour des modèles de Markov cachés
A general class of conditional U-statistics was introduced by W. Stute [3] as a generalization of the Nadaraya–Watson estimates of a regression function. It was shown that such statistics are universally consistent (Stute [3]). Also, universal consistency of the window and kn-nearest neighbor estimators (as two special cases of the conditional U-statistics) were proved by Stute [3]. In this paper, we extend these results from the independent case to dependent case.
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