Exponential inequalities for self-normalized martingales with applications

Bernard Bercu (1, 2) , Abderrahmen Touati (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability

We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pena. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.

Mots clés: Exponential inequalities; Martingales; Autoregressive processes; Branching processes

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [math.PR]

Bernard Bercu, Abderrahmen Touati. Exponential inequalities for self-normalized martingales with applications. The Annals of Applied Probability, 2008, 18, pp.1848-1869. ⟨hal-00165219⟩