# 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

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topAubry, 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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