Large deviations for quasi-arithmetically self-normalized random variables
Revised: 17 August 2010
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.
Mathematics Subject Classification: 60F10 / 62F05
Key words: Large deviations / self-normalised statistics / Bahadur exact slope
© EDP Sciences, SMAI, 2012