An invariance principle for weakly dependent stationary general models

Paul Doukhan (1, 2, 3) , Olivier Wintenberger (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 CREST - Centre de Recherche en Économie et Statistique

The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan \& Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $\theta$-weak dependence assumptions used in Dedecker \& Doukhan (2003). Here, if moments of order $>2$ exist, a weak invariance principle and convergence rates in the CLT are obtained; Doukhan \& Louhichi (1999) assumed the existence of moments with order $>4$. Besides the previously used $\eta$- and $\kappa$-weak dependence conditions, we introduce a weaker one, $\lambda$, which fits the Bernoulli shifts with dependent inputs.

Mots clés: Invariance principle; weak dependence; the Bernoulli shifts

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

Paul Doukhan, Olivier Wintenberger. An invariance principle for weakly dependent stationary general models. Probability and Mathematical Statistics, 2007, 27 (1), pp.45 - 73. ⟨hal-00359756⟩