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

Jean Bretagnolle

ESAIM: Probability and Statistics (2010)

  • Volume: 3, page 151-162
  • ISSN: 1292-8100

Abstract

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

How to cite

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Bretagnolle, Jean. "A new large deviation inequality for U-statistics of order 2." ESAIM: Probability and Statistics 3 (2010): 151-162. <http://eudml.org/doc/197738>.

@article{Bretagnolle2010,
abstract = { We prove a new large deviation inequality with applications when projecting a density on a wavelet basis. },
author = {Bretagnolle, Jean},
journal = {ESAIM: Probability and Statistics},
keywords = {Large deviations; U-statistics.; -statistics; exponential inequalities},
language = {eng},
month = {3},
pages = {151-162},
publisher = {EDP Sciences},
title = {A new large deviation inequality for U-statistics of order 2},
url = {http://eudml.org/doc/197738},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Bretagnolle, Jean
TI - A new large deviation inequality for U-statistics of order 2
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 151
EP - 162
AB - We prove a new large deviation inequality with applications when projecting a density on a wavelet basis.
LA - eng
KW - Large deviations; U-statistics.; -statistics; exponential inequalities
UR - http://eudml.org/doc/197738
ER -

References

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  1. M.A. Arcones and E. Giné, Limit Theorems for U-processes. Ann. Probab. 21 (1993) 1494-1542.  Zbl0789.60031
  2. V. De la Pe na, Decoupling and Khintchine's inequalities for U-statistics. Ann. Probab. 20 (1992) 1887-1892.  Zbl0761.60014
  3. B. Laurent, Efficient estimation of integral functionals of a density. Ann. Statist. 24 (1996) 659-681.  Zbl0859.62038
  4. B. Laurent and P. Massart, Adaptative estimation of a quadratic functional by model selection (1998) preprint.  

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