Almost sure testability of classes of densities
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- dc.contributor.author Devroye, Luc
- dc.contributor.author Lugosi, Gábor
- dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
- dc.date.accessioned 2020-05-25T09:26:49Z
- dc.date.available 2020-05-25T09:26:49Z
- dc.date.issued 1999-04-01
- dc.date.modified 2020-05-25T09:18:04Z
- dc.description.abstract Let a class $\F$ of densities be given. We draw an i.i.d.\ sample from a density $f$ which may or may not be in $\F$. After every $n$, one must make a guess whether $f \in \F$ or not. A class is almost surely testable if there exists such a testing sequence such that for any $f$, we make finitely many errors almost surely. In this paper, several results are given that allow one to decide whether a class is almost surely testable. For example, continuity and square integrability are not testable, but unimodality, log-concavity, and boundedness by a given constant are.
- dc.format.mimetype application/pdf*
- dc.identifier https://econ-papers.upf.edu/ca/paper.php?id=375
- dc.identifier.citation Journal of Nonparametric Statistics, vol. 14, pp.675--698, 2002
- dc.identifier.uri http://hdl.handle.net/10230/1024
- dc.language.iso eng
- dc.relation.ispartofseries Economics and Business Working Papers Series; 375
- dc.rights L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
- dc.subject.keyword density estimation
- dc.subject.keyword kernel estimate
- dc.subject.keyword convergence
- dc.subject.keyword testing
- dc.subject.keyword asymptotic optimality
- dc.subject.keyword minimax rate
- dc.subject.keyword minimum distance estimation
- dc.subject.keyword total boundedness
- dc.subject.keyword Statistics, Econometrics and Quantitative Methods
- dc.title Almost sure testability of classes of densities
- dc.type info:eu-repo/semantics/workingPaper