Large Deviations for Quasi-Arithmetically Self-Normalized Random Variables

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 that was obtained in the homogeneous case by Shao [14] on self- normalized statistics. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using self-normalized statistics.