Paper #375

Title:

Almost sure testability of classes of densities

Authors:

Luc Devroye and Gábor Lugosi

Date:

April 1999

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

JEL codes:

C1

Area of Research:

Statistics, Econometrics and Quantitative Methods

Published in:

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

Download the paper in PDF format