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April 2010 Confidence bands in density estimation
Evarist Giné, Richard Nickl
Ann. Statist. 38(2): 1122-1170 (April 2010). DOI: 10.1214/09-AOS738

Abstract

Given a sample from some unknown continuous density f : ℝ→ℝ, we construct adaptive confidence bands that are honest for all densities in a “generic” subset of the union of t-Hölder balls, 0<tr, 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.

Citation

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Evarist Giné. Richard Nickl. "Confidence bands in density estimation." Ann. Statist. 38 (2) 1122 - 1170, April 2010. https://doi.org/10.1214/09-AOS738

Information

Published: April 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1183.62062
MathSciNet: MR2604707
Digital Object Identifier: 10.1214/09-AOS738

Subjects:
Primary: 62G07
Secondary: 60F05

Keywords: adaptive estimation , Density estimation , Extremes , Gaussian processes , kernel estimators , limit theorem , wavelet estimators

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 2 • April 2010
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