Large deviations for quasi-arithmetically self-normalized random variables

Jean-Marie Aubry; Marguerite Zani

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 1-12
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Aubry, Jean-Marie, and Zani, Marguerite. "Large deviations for quasi-arithmetically self-normalized random variables." ESAIM: Probability and Statistics 17 (2013): 1-12. <http://eudml.org/doc/274366>.

@article{Aubry2013,
abstract = {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.},
author = {Aubry, Jean-Marie, Zani, Marguerite},
journal = {ESAIM: Probability and Statistics},
keywords = {large deviations; self-normalised statistics; Bahadur exact slope},
language = {eng},
pages = {1-12},
publisher = {EDP-Sciences},
title = {Large deviations for quasi-arithmetically self-normalized random variables},
url = {http://eudml.org/doc/274366},
volume = {17},
year = {2013},
}

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
PB - EDP-Sciences
VL - 17
SP - 1
EP - 12
AB - 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.
LA - eng
KW - large deviations; self-normalised statistics; Bahadur exact slope
UR - http://eudml.org/doc/274366
ER -

References

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