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Adaptive non-asymptotic confidence balls in density estimation

Published online by Cambridge University Press:  02 July 2012

Matthieu Lerasle
Matthieu Lerasle*
Affiliation:
Institut de Mathématiques (UMR 5219), INSA de Toulouse, Université de Toulouse, France. lerasle@gmail.com
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Abstract

We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.

Keywords

Confidence ballsdensity estimationresampling methods
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 16 , 2012 , pp. 61 - 85
Copyright
© EDP Sciences, SMAI, 2012

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