Sharp large deviations under Bernstein's condition

Xiequan Fan (1, 2) , Ion Grama (3) , Quansheng Liu (3)

1 Regularity - Probabilistic modelling of irregularity and application to uncertainties management
2 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
3 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We improve Bernstein's inequality for sums of non-bounded random variables. In particular, we establish a sharp large deviation expansion similar to that of Cramér and Bahadur-Rao.

Mots clés: Bahadur-Rao theorem; Cramér theorem; Sharp large deviations; Bernstein's inequality

Domaines: Probabilités [math.PR]

Xiequan Fan, Ion Grama, Quansheng Liu. Sharp large deviations under Bernstein's condition. Comptes rendus hebdomadaires des séances de l'Académie des sciences, 2013, 351, pp.845-848. ⟨10.1016/j.crma.2013.10.015⟩. ⟨hal-00905527⟩