Adaptive non-asymptotic confidence balls in density estimation
ESAIM: Probability and Statistics, Tome 16 (2012), pp. 61-85

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.

DOI : 10.1051/ps/2010012
Classification : 62G07, 62G09, 62G10, 62G15
Keywords: confidence balls, density estimation, resampling methods 
@article{PS_2012__16__61_0,
     author = {Lerasle, Matthieu},
     title = {Adaptive non-asymptotic confidence balls in density estimation},
     journal = {ESAIM: Probability and Statistics},
     pages = {61--85},
     year = {2012},
     publisher = {EDP Sciences},
     volume = {16},
     doi = {10.1051/ps/2010012},
     mrnumber = {2946120},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2010012/}
}
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Lerasle, Matthieu. Adaptive non-asymptotic confidence balls in density estimation. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 61-85. doi: 10.1051/ps/2010012

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