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self-normalised statistics

ESAIM: Probability and Statistics (1)

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Large deviations for quasi-arithmetically self-normalizedrandom variables
Jean-Marie Aubry, Marguerite Zani
Journal:

ESAIM: Probability and Statistics / Volume 17 / 2013

Published online by Cambridge University Press:

06 December 2012, pp. 1-12

Print publication:

2013
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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.