# Adaptive estimation of a quadratic functional of a density by model selection

ESAIM: Probability and Statistics (2005)

- Volume: 9, page 1-18
- ISSN: 1292-8100

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topLaurent, Béatrice. "Adaptive estimation of a quadratic functional of a density by model selection." ESAIM: Probability and Statistics 9 (2005): 1-18. <http://eudml.org/doc/245507>.

@article{Laurent2005,

abstract = {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 $\int _\{\mathbb \{R\}\} f^2(x)\{\rm d\}x$ 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.},

author = {Laurent, Béatrice},

journal = {ESAIM: Probability and Statistics},

keywords = {adaptive estimation; quadratic functionals; model selection; Besov bodies; efficient estimation; Adaptive estimation},

language = {eng},

pages = {1-18},

publisher = {EDP-Sciences},

title = {Adaptive estimation of a quadratic functional of a density by model selection},

url = {http://eudml.org/doc/245507},

volume = {9},

year = {2005},

}

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

PB - EDP-Sciences

VL - 9

SP - 1

EP - 18

AB - 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 $\int _{\mathbb {R}} f^2(x){\rm d}x$ 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.

LA - eng

KW - adaptive estimation; quadratic functionals; model selection; Besov bodies; efficient estimation; Adaptive estimation

UR - http://eudml.org/doc/245507

ER -

## References

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