| Issue |
ESAIM: PS
Volume 15, 2011
|
|
|---|---|---|
| Page(s) | 168 - 179 | |
| DOI | https://doi.org/10.1051/ps/2009014 | |
| Published online | 05 January 2012 | |
Cramér type moderate deviations for Studentized U-statistics*,**,***
1
Department of Statistics, Stanford University Stanford, CA CA 94305-4065, USA;
This email address is being protected from spambots. You need JavaScript enabled to view it.
2
Department of Mathematics, Hong Kong University of Science and Technology,
Clear Water Bay, Kowloon
Hong Kong, P.R. China; This email address is being protected from spambots. You need JavaScript enabled to view it.
3
School of Mathematics and Statistics,
University of Sydney,
NSW 2006, Australia;
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
20
September
2008
Revised:
2
June
2009
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.
Mathematics Subject Classification: 60F10 / 60F05
Key words: Moderate deviation / u-statistic / studentized
Research partially supported by NSF-MCS-0305749.
Research partially supported by Hong Kong RGC – CERG 602206 and 602608.
Research partially supported by an Australian Research Council (ARC) discovery project.
© EDP Sciences, SMAI, 2011
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