Title :

Functional Limit Theorem for the Empirical Process of a Class of Bernoulli Shifts with Long Memory

Author(s) :

Doukhan, Paul [Auteur]
Statistique Appliquée et MOdélisation Stochastique [SAMOS]
Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques [MATISSE - UMR 8595]
Lang, Gabriel [Auteur]
Laboratoire de Gestion du Risque En Sciences de l'Environnement [GRESE]
Surgailis, Donatas [Auteur]
Viano, Marie Claude [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Theoretical Probability

Pages :

161-186

Publisher :

Springer

Publication date :

2005

ISSN :

0894-9840

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

We prove a functional central limit theorem for the empirical process of a stationary process $X_t = Y_t + V_t$, where $Y_t$ is a long memory moving average in i.i.d. r.v.'s $\zeta_s, s\le t $, and $V_t = V(\zeta_t, ...
Show more >We prove a functional central limit theorem for the empirical process of a stationary process $X_t = Y_t + V_t$, where $Y_t$ is a long memory moving average in i.i.d. r.v.'s $\zeta_s, s\le t $, and $V_t = V(\zeta_t, \zeta_{t-1}, \dots )$ is a weakly dependent nonlinear Bernoulli shift. Conditions of weak dependence of $V_t$ are written in terms of $L^2-$norms of shift-cut differences $ V(\zeta_t, \dots, \zeta_{t-n}, 0, \dots, ) - V(\zeta_t, \dots, \zeta_{t-n+1}, 0, \dots )$. Examples of Bernoulli shifts are discussed. The limit empirical process is a degenerated process of the form $f(x) Z $, where $f$ is the marginal p.d.f. of $X_0$ and $Z $ is a standard normal r.v. The proof is based on a uniform reduction principle for the empirical process.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL