Institut de Mathématiques (UMR 5219), INSA de Toulouse, Université de Toulouse, France. email@example.com
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.
(Received November 14 2008)
(Revised January 11 2010)
(Online publication July 02 2012)
Mathematics Subject Classification: