{"title":"Goodness of fit testing using a specific density estimate","authors":"C. Albers, W. Schaafsma","doi":"10.1524/STND.2008.0909","DOIUrl":"https://doi.org/10.1524/STND.2008.0909","url":null,"abstract":"To test the hypothesis H0: f=ψ that an unknown density f is equal to a specified one, ψ, an estimate f^ of f is compared with ψ. The total variation distance ∥ f^-ψ∥1 is used as test statistic.","PeriodicalId":380446,"journal":{"name":"Statistics & Decisions","volume":"427 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115258520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Oracle inequalities for multi-fold cross validation","authors":"A. Vaart, S. Dudoit, M. Laan","doi":"10.1524/STND.2006.24.3.351","DOIUrl":"https://doi.org/10.1524/STND.2006.24.3.351","url":null,"abstract":"We consider choosing an estimator or model from a given class by cross validation consisting of holding a nonneglible fraction of the observations out as a test set. We derive bounds that show that the risk of the resulting procedure is (up to a constant) smaller than the risk of an oracle plus an error which typically grows logarithmically with the number of estimators in the class. We extend the results to penalized cross validation in order to control unbounded loss functions. Applications include regression with squared and absolute deviation loss and classification under Tsybakov’s condition.","PeriodicalId":380446,"journal":{"name":"Statistics & Decisions","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124307768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Schweizer, T. Wien, Versicherungsmathematik Departement, Fam ETH-Zentrum
{"title":"Dynamic utility-based good deal bounds","authors":"M. Schweizer, T. Wien, Versicherungsmathematik Departement, Fam ETH-Zentrum","doi":"10.1524/STND.2007.0905","DOIUrl":"https://doi.org/10.1524/STND.2007.0905","url":null,"abstract":"We introduce and study no-good-deal valuation bounds deflned in terms of ex- pected utility. A utility-based good deal is a payofi whose expected utility is too high in comparison to the utility of its price. Forbidding good deals induces, via duality, restrictions on pricing kernels and thereby gives tighter valuation bounds on payofis than absence of arbitrage alone. Our approach extends earlier work by • Cern¶ (2003) in several directions: We give rigorous results for a general proba- bility space instead of flnite ›; we systematically use duality results to provide a streamlined approach with simple arguments; we do all this rigorously for both static and dynamic situations; and we give a systematic comparison between local and global (conditional) pricing kernel restrictions for the temporally dynamic setting. For the dynamic case, we show in a Levy framework that deflning no- good-deal valuation measures by imposing local conditional restrictions on their instantaneous market prices of risk gives valuation bounds having very good dy- namic properties as processes over time. We also show that global restrictions cannot yield such results in general.","PeriodicalId":380446,"journal":{"name":"Statistics & Decisions","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116189683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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