Self normalized central limit theorem for some mixing processes

Manel Kacem (1) , Véronique Maume-Deschamps (2, 3)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 ICJ - Institut Camille Jordan
3 PSPM - Probabilités, statistique, physique mathématique

We prove a self normalized central limit theorem for a new mixing class of processes introduced in Kacem et al. (2013). This class is larger than the classical strongly mixing processes and thus our result is more general than Peligrad and Shao's (1995) and Shi's (2000) ones. The fact that some conditionally independent processes satisfy this kind of mixing properties motivated our study. We investigate the weak consistency as well as the asymptotic normality of the estimator of the variance that we propose.

Mots clés: Self normalized central limit theorem; Mixing processes; Variance estimation; Invariance principle

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

Manel Kacem, Véronique Maume-Deschamps. Self normalized central limit theorem for some mixing processes. 2014. ⟨hal-00927113⟩