Paper #375
- Títol:
- Almost sure testability of classes of densities
- Autors:
- Luc Devroye i Gábor Lugosi
- Data:
- Abril 1999
- Resum:
- 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.
- Paraules clau:
- Density estimation, kernel estimate, convergence, testing, asymptotic optimality, minimax rate, minimum distance estimation, total boundedness
- Codis JEL:
- C1
- Àrea de Recerca:
- Estadística, Econometria i Mètodes Quantitatius
- Publicat a:
- Journal of Nonparametric Statistics, vol. 14, pp.675--698, 2002
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