Dependent Lindeberg central limit theorem and some applications

Details Dependent Lindeberg central limit theorem and some applications Dependent Lindeberg central limit theorem and some applications

2007-01-30

arxiv.org/abs/math/0701872v1

Mathematics

Statistics Theory

Scientific paper

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.

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