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Dependent Lindeberg central limit theorem and some applications. (English) Zbl 1187.60013

Summary: 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 P. Doukhan and S. Louhichi [Stochastic Processes Appl. 84, No. 2, 313–342 (1999; Zbl 0996.60020)], 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, \(\ldots\), enter this frame.

MSC:

60F05 Central limit and other weak theorems
62G07 Density estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G09 Nonparametric statistical resampling methods

Citations:

Zbl 0996.60020
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References:

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