Geodesic
Cramér type moderate deviations for Studentized U-statistics
ESAIM: Probability and Statistics, Tome 15 (2011), pp. 168-179

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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.

DOI : 10.1051/ps/2009014
Classification : 60F10, 60F05
Keywords: moderate deviation, u-statistic, studentized 
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     author = {Lai, Tze Leng and Shao, Qi-Man and Wang, Qiying},
     title = {Cram\'er type moderate deviations for {Studentized} {U-statistics}},
     journal = {ESAIM: Probability and Statistics},
     pages = {168--179},
     publisher = {EDP-Sciences},
     volume = {15},
     year = {2011},
     doi = {10.1051/ps/2009014},
     mrnumber = {2870510},
     zbl = {1271.60044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2009014/}
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Lai, Tze Leng; Shao, Qi-Man; Wang, Qiying. Cramér type moderate deviations for Studentized U-statistics. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 168-179. doi: 10.1051/ps/2009014

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