| Issue |
ESAIM: PS
Volume 9, June 2005
|
|
|---|---|---|
| Page(s) | 1 - 18 | |
| DOI | https://doi.org/10.1051/ps:2005001 | |
| Published online | 15 November 2005 | |
Adaptive estimation of a quadratic functional of a density by model selection
INSA-LSP. Departement GMM,
135 avenue de Rangueil, 31077 Toulouse Cedex 4, France; beatrice.laurent@insa-toulouse.fr
Received:
23
October
2003
Revised:
16
July
2004
We consider the problem of estimating the integral of the square of a density
f from the observation of a n 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 U-statistics of order 2 due to Houdré and Reynaud.
Mathematics Subject Classification: 62G05 / 62G20 / 62J02
Key words: Adaptive estimation / quadratic functionals / model selection / Besov bodies / efficient estimation.
© EDP Sciences, SMAI, 2005
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