{"title":"General tests of independence based on empirical processes indexed by functions","authors":"Salim Bouzebda","doi":"10.1016/j.stamet.2014.03.001","DOIUrl":null,"url":null,"abstract":"<div><p>The present paper is mainly concerned with the statistical tests of the independence problem between random vectors. We develop an approach based on general empirical processes indexed by a particular class of functions. We prove two abstract approximation theorems<span> that include some existing results as particular cases. Finally, we characterize the limiting behavior of the Möbius transformation of empirical processes indexed by functions under contiguous sequences of alternatives.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"21 ","pages":"Pages 59-87"},"PeriodicalIF":0.0000,"publicationDate":"2014-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2014.03.001","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572312714000276","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 9
Abstract
The present paper is mainly concerned with the statistical tests of the independence problem between random vectors. We develop an approach based on general empirical processes indexed by a particular class of functions. We prove two abstract approximation theorems that include some existing results as particular cases. Finally, we characterize the limiting behavior of the Möbius transformation of empirical processes indexed by functions under contiguous sequences of alternatives.
期刊介绍：
Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.
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