Adaptive non-asymptotic confidence balls in density estimation

2010/07/26 by Matthieu Lerasle, Lerasle, Matthieu
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1007.4528

arxiv created 2010/07/26 · arxiv updated 2010/07/27

Abstract

We build confidence balls for the common density s of a real valued sample X₁,...,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≥2 and the balls are adaptive over a collection of linear spaces.

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