Adaptive non-asymptotic confidence balls in density estimation

Matthieu Lerasle

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arXiv · 1007.4528

Adaptive non-asymptotic confidence balls in density estimation

Matthieu Lerasle

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Abstract

We build confidence balls for the common density $s$ of a real valued sample $X_1,...,X_n$. 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 $n\geq2$ and the balls are adaptive over a collection of linear spaces.

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Matthieu Lerasle. 2010-07-26. Adaptive non-asymptotic confidence balls in density estimation. https://arxiv.org/abs/1007.4528

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