Probability theory/Statistics
Sharp large deviations under Bernsteinʼs condition
Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 845-848.

We improve Bernsteinʼs 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.

Nous améliorons lʼinégalité de Bernstein pour les sommes de variables aléatoires non bornées. En particulier, nous établissons un développement de grandes déviations précises de type Cramér et Bahadur–Rao.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.015
Fan, Xiequan 1, 2; Grama, Ion 1; Liu, Quansheng 1

1 Université de Bretagne-Sud, UMR 6205, LMBA, 56000 Vannes, France
2 Regularity Team, Inria and MAS Laboratory, École centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France
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Fan, Xiequan; Grama, Ion; Liu, Quansheng. Sharp large deviations under Bernsteinʼs condition. Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 845-848. doi : 10.1016/j.crma.2013.10.015. http://www.numdam.org/articles/10.1016/j.crma.2013.10.015/

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