Exponential inequalities and functional estimations for weak dependent datas ; applications to dynamical systems.

Véronique Maume-Deschamps (1, 2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 SAF - Laboratoire de Sciences Actuarielle et Financière

We estimate density and regression functions for weak dependant datas. Using an exponential inequality obtained by Dedecker and Prieur and in a previous article of the author, we control the deviation between the estimator and the function itself. These results are applied to a large class of dynamical systems and lead to estimations of invariant densities and on the mapping itself.

Mots clés: Exponential inequalities; functional estimation; dynamical systems; weak dependance

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

Véronique Maume-Deschamps. Exponential inequalities and functional estimations for weak dependent datas ; applications to dynamical systems.. Stoch. Dyn., 2006, pp.535. ⟨10.1142/S0219493706001876⟩. ⟨hal-00022453⟩