Almost sure testability of classes of densities

Luc Devroye and Gabor Lugosi

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

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.

Keywords: Density estimation; kernel estimate; convergence; testing; asymptotic optimality; minimax rate; minimum distance estimation; total boundedness (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 1999-04
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:375

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