Large deviations for quasi-arithmetically self-normalized random variables
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 1-12.

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

DOI : 10.1051/ps/2011112
Classification : 60F10, 62F05
Mots clés : large deviations, self-normalised statistics, Bahadur exact slope 
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Aubry, Jean-Marie; Zani, Marguerite. Large deviations for quasi-arithmetically self-normalized random variables. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 1-12. doi : 10.1051/ps/2011112. http://www.numdam.org/articles/10.1051/ps/2011112/

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