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Cramér type moderate deviations for Studentized U-statistics******

Published online by Cambridge University Press:  05 January 2012

Tze Leng Lai ,
Qi-Man Shao  and
Qiying Wang
Tze Leng Lai
Affiliation:
Department of Statistics, Stanford University Stanford, CA CA 94305-4065, USA; lait@stanford.edu
Qi-Man Shao
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon Hong Kong, P.R. China; maqmshao@ust.hk
Qiying Wang
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia; qiying@maths.usyd.edu.au
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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.

Keywords

Moderate deviationu-statisticstudentized
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. 168 - 179
Copyright
© EDP Sciences, SMAI, 2011

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