Paper #375

Título:

Almost sure testability of classes of densities

Autores:

Luc Devroye y Gábor Lugosi

Data:

Abril 1999

Resumen:

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.

Palabras clave:

Density estimation, kernel estimate, convergence, testing, asymptotic optimality, minimax rate, minimum distance estimation, total boundedness

Códigos JEL:

C1

Área de investigación:

Estadística, Econometría y Métodos Cuantitativos

Publicado en:

Journal of Nonparametric Statistics, vol. 14, pp.675--698, 2002

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