1 results
Adaptive estimation of a quadratic functional of a density by model selection
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- Journal:
- ESAIM: Probability and Statistics / Volume 9 / February 2005
- Published online by Cambridge University Press:
- 15 November 2005, pp. 1-18
- Print publication:
- February 2005
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- Article
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We consider the problem of estimating the integral of the square of a densityf from the observation of a n sample. Our method to estimate $\int_{\mathbb{R}} f^2(x){\rm d}x$
isbased 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 exponentialinequality for U-statistics of order 2 due to Houdré and Reynaud.
