Displaying similar documents to “Nonparametric density estimators based on nonstationary absolutely regular random sequences.”

Dependent Lindeberg central limit theorem and some applications

Jean-Marc Bardet, Paul Doukhan, Gabriel Lang, Nicolas Ragache (2008)

ESAIM: Probability and Statistics


In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the...