Adaptive non-asymptotic confidence balls in density estimation

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 $n\ge 2$ and the balls are adaptive over a collection of linear spaces.

References in corpus (1)

• Model selection by resampling penalization