{"title":"Semiparametric Testing of Statistical Functionals Revisited","authors":"V. Ostrovski","doi":"10.2139/ssrn.2287633","DOIUrl":null,"url":null,"abstract":"Abstract Along the lines of Janssen's and Pfanzagl's work the testing theory for statistical functionals is further developed for non-parametric one-sample problems. Efficient tests for the one-sided and two-sided problems are derived for nonparametric statistical functionals. The asymptotic power function is calculated under implicit alternatives and hypotheses, which are given by the functional itself, for the one-sided and two-sided cases. Under mild regularity assumptions is shown that these tests are asymptotic most powerful. The combination of the modern theory of Le Cam and approximation in limit experiments provide a deep insight into the upper bounds for asymptotic power functions tests for the one-sided and two-sided problems of hypothesis testing. As example tests concerning the von Mises functional are treated in nonparametric context.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2012-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ERN: Semiparametric & Nonparametric Methods (Topic)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.2287633","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Along the lines of Janssen's and Pfanzagl's work the testing theory for statistical functionals is further developed for non-parametric one-sample problems. Efficient tests for the one-sided and two-sided problems are derived for nonparametric statistical functionals. The asymptotic power function is calculated under implicit alternatives and hypotheses, which are given by the functional itself, for the one-sided and two-sided cases. Under mild regularity assumptions is shown that these tests are asymptotic most powerful. The combination of the modern theory of Le Cam and approximation in limit experiments provide a deep insight into the upper bounds for asymptotic power functions tests for the one-sided and two-sided problems of hypothesis testing. As example tests concerning the von Mises functional are treated in nonparametric context.