Adaptive non-asymptotic confidence balls in density estimation
Institut de Mathématiques (UMR 5219), INSA de Toulouse, Université de Toulouse, France
Received: 14 November 2008
Revised: 11 January 2010
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.
Mathematics Subject Classification: 62G07 / 62G09 / 62G10 / 62G15
Key words: Confidence balls / density estimation / resampling methods
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