Cramér type moderate deviations for Studentized U-statistics

Tze Leng Lai; Qi-Man Shao; Qiying Wang

ESAIM: Probability and Statistics (2011)

  • Volume: 15, page 168-179
  • ISSN: 1292-8100

Abstract

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Let Tn be a Studentized U-statistic. It is proved that a Cramér type moderate deviation P(Tn ≥ x)/(1 − Φ(x)) → 1 holds uniformly in x ∈ [0, o(n1/6)) when the kernel satisfies some regular conditions.

How to cite

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Lai, Tze Leng, Shao, Qi-Man, and Wang, Qiying. "Cramér type moderate deviations for Studentized U-statistics." ESAIM: Probability and Statistics 15 (2011): 168-179. <http://eudml.org/doc/277141>.

@article{Lai2011,
abstract = {Let Tn be a Studentized U-statistic. It is proved that a Cramér type moderate deviation P(Tn ≥ x)/(1 − Φ(x)) → 1 holds uniformly in x ∈ [0, o(n1/6)) when the kernel satisfies some regular conditions.},
author = {Lai, Tze Leng, Shao, Qi-Man, Wang, Qiying},
journal = {ESAIM: Probability and Statistics},
keywords = {moderate deviation; u-statistic; studentized; -statistic; Studentized statistic},
language = {eng},
pages = {168-179},
publisher = {EDP-Sciences},
title = {Cramér type moderate deviations for Studentized U-statistics},
url = {http://eudml.org/doc/277141},
volume = {15},
year = {2011},
}

TY - JOUR
AU - Lai, Tze Leng
AU - Shao, Qi-Man
AU - Wang, Qiying
TI - Cramér type moderate deviations for Studentized U-statistics
JO - ESAIM: Probability and Statistics
PY - 2011
PB - EDP-Sciences
VL - 15
SP - 168
EP - 179
AB - Let Tn be a Studentized U-statistic. It is proved that a Cramér type moderate deviation P(Tn ≥ x)/(1 − Φ(x)) → 1 holds uniformly in x ∈ [0, o(n1/6)) when the kernel satisfies some regular conditions.
LA - eng
KW - moderate deviation; u-statistic; studentized; -statistic; Studentized statistic
UR - http://eudml.org/doc/277141
ER -

References

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