Probability and moment inequalities for sums of weakly dependent random variables, with applications

Paul Doukhan (1, 2) , Michael Neumann (3)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 IENA - Institut fur Stochastik Ernst Friedrich-Schiller-Universitat Jena

Using the idea of weak dependence introduced in Doukhan and Louhichi 1999, we present a new Bernstein type inequality for times series. This result extends on Kallabis and Neumann 2004 but it also holds for non causal type sequences and subgeometric decay rates of the dependence coefficients. Examples of applications and a large variety of models beyond mixing times series are also listed.

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

Paul Doukhan, Michael Neumann. Probability and moment inequalities for sums of weakly dependent random variables, with applications. Stochastic Processes and their Applications, 2007, 117 (7), pp.878-903. ⟨10.1016/j.spa.2006.10.011⟩. ⟨hal-00141587⟩