Rates in the empirical central limit theorem for stationary weakly dependent random fields - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2002

Rates in the empirical central limit theorem for stationary weakly dependent random fields

Résumé

A weak dependence condition is derived as the natural generalization to random fields on notions developed in Doukhan and Louhichi (1999). Examples of such weakly dependent fields are defined. In the context of a weak dependence coefficient series with arithmetic or geometric decay, we give explicit bounds in Prohorov metric for the convergence in the empirical central limit theorem. For random fields indexed by Zd , in the geometric decay case, rates have the form n−1/(8d+24) L(n), where L(n) is a power of log(n).

Dates et versions

hal-02677505 , version 1 (31-05-2020)

Identifiants

Citer

Paul Doukhan, Gabriel Lang. Rates in the empirical central limit theorem for stationary weakly dependent random fields. Statistical Inference for Stochastic Processes, 2002, 5 (2), pp.199-228. ⟨10.1023/A:1016396906927⟩. ⟨hal-02677505⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More