{"title":"伯恩斯坦条件共线估计器","authors":"Noël Veraverbeke","doi":"10.1007/s00362-024-01573-x","DOIUrl":null,"url":null,"abstract":"<p>The use of Bernstein polynomials in smooth nonparametric estimation of copulas has been well established in recent years. Their good properties in terms of bias and variance are well known. In this note we generalize some of the asymptotic theory to conditional copulas, that is where the dependence structure between the variables changes with a value of a random covariate. We obtain asymptotic representations and asymptotic normality for a conditional copula.</p>","PeriodicalId":51166,"journal":{"name":"Statistical Papers","volume":"56 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bernstein estimator for conditional copulas\",\"authors\":\"Noël Veraverbeke\",\"doi\":\"10.1007/s00362-024-01573-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The use of Bernstein polynomials in smooth nonparametric estimation of copulas has been well established in recent years. Their good properties in terms of bias and variance are well known. In this note we generalize some of the asymptotic theory to conditional copulas, that is where the dependence structure between the variables changes with a value of a random covariate. We obtain asymptotic representations and asymptotic normality for a conditional copula.</p>\",\"PeriodicalId\":51166,\"journal\":{\"name\":\"Statistical Papers\",\"volume\":\"56 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistical Papers\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00362-024-01573-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Papers","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00362-024-01573-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
The use of Bernstein polynomials in smooth nonparametric estimation of copulas has been well established in recent years. Their good properties in terms of bias and variance are well known. In this note we generalize some of the asymptotic theory to conditional copulas, that is where the dependence structure between the variables changes with a value of a random covariate. We obtain asymptotic representations and asymptotic normality for a conditional copula.
期刊介绍：
The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.
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