Adaptive estimation of a quadratic functional of a density by model selection
ESAIM: Probability and Statistics, Tome 9 (2005), pp. 1-18
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We consider the problem of estimating the integral of the square of a density from the observation of a sample. Our method to estimate is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for -statistics of order 2 due to Houdré and Reynaud.
DOI :
10.1051/ps:2005001
Classification :
62G05, 62G20, 62J02
Keywords: adaptive estimation, quadratic functionals, model selection, Besov bodies, efficient estimation
Keywords: adaptive estimation, quadratic functionals, model selection, Besov bodies, efficient estimation
@article{PS_2005__9__1_0, author = {Laurent, B\'eatrice}, title = {Adaptive estimation of a quadratic functional of a density by model selection}, journal = {ESAIM: Probability and Statistics}, pages = {1--18}, publisher = {EDP-Sciences}, volume = {9}, year = {2005}, doi = {10.1051/ps:2005001}, mrnumber = {2148958}, zbl = {1136.62333}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2005001/} }
TY - JOUR AU - Laurent, Béatrice TI - Adaptive estimation of a quadratic functional of a density by model selection JO - ESAIM: Probability and Statistics PY - 2005 SP - 1 EP - 18 VL - 9 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2005001/ DO - 10.1051/ps:2005001 LA - en ID - PS_2005__9__1_0 ER -
%0 Journal Article %A Laurent, Béatrice %T Adaptive estimation of a quadratic functional of a density by model selection %J ESAIM: Probability and Statistics %D 2005 %P 1-18 %V 9 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2005001/ %R 10.1051/ps:2005001 %G en %F PS_2005__9__1_0
Laurent, Béatrice. Adaptive estimation of a quadratic functional of a density by model selection. ESAIM: Probability and Statistics, Tome 9 (2005), pp. 1-18. doi: 10.1051/ps:2005001
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