Rates of convergence for minimal distances in the central limit theorem under projective criteria

Jérôme Dedecker (1) , Florence Merlevède (2) , Emmanuel Rio (3)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 LMV - Laboratoire de Mathématiques de Versailles

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

Mots clés: rates of convergence; minimal and ideal distances; Martingale difference sequences; stationary sequences; projective criteria; weak dependence; uniform mixing

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

Jérôme Dedecker, Florence Merlevède, Emmanuel Rio. Rates of convergence for minimal distances in the central limit theorem under projective criteria. Electronic Communications in Probability, 2009, 14, pp.978-1011. ⟨10.1214/EJP.v14-648⟩. ⟨hal-00193533⟩