The empirical distribution function for dependent variables: asymptotic and non asymptotic results in L^p

Jerome Dedecker (1) , F. Merlevède (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Considering the centered empirical distribution function F n-F as a variable in L^p(mu) , we derive non asymptotic upper bounds for the deviation of the L^p(mu) -norms of F n-F as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.

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

Jerome Dedecker, F. Merlevède. The empirical distribution function for dependent variables: asymptotic and non asymptotic results in L^p. ESAIM: Probability and Statistics, 2007, 11, pp.102-114. ⟨hal-00686009⟩