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Large deviations for quasi-arithmetically self-normalizedrandom variables

Published online by Cambridge University Press:  06 December 2012

Jean-Marie Aubry  and
Marguerite Zani
Jean-Marie Aubry
Affiliation:
Laboratoire d’Analyse et Mathématiques Appliquées (CNRS UMR 8050), Université Paris-Est Créteil, 61 av. du Général de Gaulle, 94010 Créteil Cedex, France;. jmaubry@math.cnrs.fr; zani@u-pec.fr
Marguerite Zani
Affiliation:
Laboratoire d’Analyse et Mathématiques Appliquées (CNRS UMR 8050), Université Paris-Est Créteil, 61 av. du Général de Gaulle, 94010 Créteil Cedex, France;. jmaubry@math.cnrs.fr; zani@u-pec.fr
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Abstract

We introduce a family of convex (concave) functions called sup (inf) of powers, which areused as generator functions for a special type of quasi-arithmetic means. Using thesemeans, we generalize the large deviation result on self-normalized statistics that wasobtained in the homogeneous case by [Q.-M. Shao, Self-normalized large deviations.Ann. Probab. 25 (1997) 285–328]. Furthermore, in thehomogenous case, we derive the Bahadur exact slope for tests using self-normalizedstatistics.

Keywords

Large deviationsself-normalised statisticsBahadur exact slope

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 1 - 12
Copyright
© EDP Sciences, SMAI, 2012

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References

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