Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-16T14:29:48.110Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.