Dependent Lindeberg central limit theorem and some applications

Bardet, Jean-Marc; Doukhan, Paul; Lang, Gabriel; Ragache, Nicolas

ESAIM: Probability and Statistics, Tome 12 (2008), pp. 154-172.

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 usual causal or non causal time series: gaussian, associated, linear, ARCH($\infty$), bilinear, Volterra processes, $...$, enter this frame.

Classification : 60F05, 62G07, 62M10, 62G09
Mots clés : central limit theorem, Lindeberg method, weak dependence, kernel density estimation, subsampling

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