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.
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}, publisher = {EDP-Sciences}, volume = {16}, year = {2012}, doi = {10.1051/ps/2010012}, mrnumber = {2946120}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2010012/} }
TY - JOUR AU - Lerasle, Matthieu TI - Adaptive non-asymptotic confidence balls in density estimation JO - ESAIM: Probability and Statistics PY - 2012 SP - 61 EP - 85 VL - 16 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2010012/ DO - 10.1051/ps/2010012 LA - en ID - PS_2012__16__61_0 ER -
Lerasle, Matthieu. Adaptive non-asymptotic confidence balls in density estimation. ESAIM: Probability and Statistics, Volume 16 (2012), pp. 61-85. doi : 10.1051/ps/2010012. http://archive.numdam.org/articles/10.1051/ps/2010012/
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