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A new large deviation inequality for U-statistics of order 2

Published online by Cambridge University Press:  15 August 2002

Jean Bretagnolle
Jean Bretagnolle*
Affiliation:
URAD 0743, Université d'Orsay, bâtiment 425, 91405 Orsay Cedex, France; Jean.Bretagnolle@math.u-psud.fr.
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Abstract

We prove a new large deviation inequality with applications when projecting a density on a wavelet basis.

Keywords

Large deviationsU-statistics.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 3 , 1999 , pp. 151 - 162
Copyright
© EDP Sciences, SMAI, 1999

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References

Arcones, M.A. and Giné, E., Limit Theorems for U-processes. Ann. Probab . 21 (1993) 1494-1542. CrossRef
De la Pe, V. na, Decoupling and Khintchine's inequalities for U-statistics. Ann. Probab . 20 (1992) 1887-1892.
Laurent, B., Efficient estimation of integral functionals of a density. Ann. Statist . 24 (1996) 659-681.
B. Laurent and P. Massart, Adaptative estimation of a quadratic functional by model selection (1998) preprint.