Large Deviations for Quasi-Arithmetically Self-Normalized Random Variables

Jean-Marie Aubry (1) , Marguerite Zani (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Probabilités [math.PR]

Jean-Marie Aubry, Marguerite Zani. Large Deviations for Quasi-Arithmetically Self-Normalized Random Variables. ESAIM: Probability and Statistics, 2013, 17 (1), pp.1--12. ⟨hal-00796315⟩