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confidence balls

ESAIM: Probability and Statistics (1)

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1 results

Adaptive non-asymptotic confidence balls in density estimation
Matthieu Lerasle
Journal:

ESAIM: Probability and Statistics / Volume 16 / 2012

Published online by Cambridge University Press:

02 July 2012, pp. 61-85

Print publication:

2012
- Article
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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.