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arXiv · 1002.4801

Confidence bands in density estimation

Evarist Giné·Richard Nickl
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Abstract

Given a sample from some unknown continuous density $f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are honest for all densities in a "generic" subset of the union of $t$-Hölder balls, $0<t\le r$, where $r$ is a fixed but arbitrary integer. The exceptional ("nongeneric") set of densities for which our results do not hold is shown to be nowhere dense in the relevant Hölder-norm topologies. In the course of the proofs we also obtain limit theorems for maxima of linear wavelet and kernel density estimators, which are of independent interest.

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Evarist Giné, Richard Nickl. 2010-02-25. Confidence bands in density estimation. https://doi.org/10.1214/09-aos738

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