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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.
@article{PS_2013__17__1_0,
author = {Aubry, Jean-Marie and Zani, Marguerite},
title = {Large deviations for quasi-arithmetically self-normalized random variables},
journal = {ESAIM: Probability and Statistics},
pages = {1--12},
publisher = {EDP-Sciences},
volume = {17},
year = {2013},
doi = {10.1051/ps/2011112},
mrnumber = {3002993},
zbl = {1290.60028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011112/}
}
TY - JOUR AU - Aubry, Jean-Marie AU - Zani, Marguerite TI - Large deviations for quasi-arithmetically self-normalized random variables JO - ESAIM: Probability and Statistics PY - 2013 SP - 1 EP - 12 VL - 17 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps/2011112/ DO - 10.1051/ps/2011112 LA - en ID - PS_2013__17__1_0 ER -
%0 Journal Article %A Aubry, Jean-Marie %A Zani, Marguerite %T Large deviations for quasi-arithmetically self-normalized random variables %J ESAIM: Probability and Statistics %D 2013 %P 1-12 %V 17 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps/2011112/ %R 10.1051/ps/2011112 %G en %F PS_2013__17__1_0
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
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