Adaptive non-asymptotic confidence balls in density estimation

Matthieu Lerasle

Adaptive non-asymptotic confidence balls in density estimation

Statistics Theory 2010-07-27 v1 Statistics Theory

Authors: Matthieu Lerasle

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.

Keywords

density estimation statistical inference nonparametric regression

Cite

@article{arxiv.1007.4528,
  title  = {Adaptive non-asymptotic confidence balls in density estimation},
  author = {Matthieu Lerasle},
  journal= {arXiv preprint arXiv:1007.4528},
  year   = {2010}
}

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