Devroye, LucLugosi, GáborUniversitat Pompeu Fabra. Departament d'Economia i Empresa2020-05-252020-05-251999-04-01Journal of Nonparametric Statistics, vol. 14, pp.675--698, 2002http://hdl.handle.net/10230/1024Let 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.application/pdfengL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commonsinfo:eu-repo/semantics/workingPaperdensity estimationkernel estimateconvergencetestingasymptotic optimalityminimax rateminimum distance estimationtotal boundednessStatistics, Econometrics and Quantitative Methodsinfo:eu-repo/semantics/openAccess