# Dependent Lindeberg central limit theorem and some applications

• Volume: 12, page 154-172
• ISSN: 1292-8100

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## Abstract

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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(∞), bilinear, Volterra processes, ..., enter this frame.

## How to cite

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Bardet, Jean-Marc, et al. "Dependent Lindeberg central limit theorem and some applications ." ESAIM: Probability and Statistics 12 (2008): 154-172. <http://eudml.org/doc/250399>.

@article{Bardet2008,
abstract = { 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(∞), bilinear, Volterra processes, ..., enter this frame. },
author = {Bardet, Jean-Marc, Doukhan, Paul, Lang, Gabriel, Ragache, Nicolas},
journal = {ESAIM: Probability and Statistics},
keywords = {Central limit theorem; Lindeberg method; weak dependence; kernel density estimation; subsampling; central limit theorem},
language = {eng},
month = {1},
pages = {154-172},
publisher = {EDP Sciences},
title = {Dependent Lindeberg central limit theorem and some applications },
url = {http://eudml.org/doc/250399},
volume = {12},
year = {2008},
}

TY - JOUR
AU - Bardet, Jean-Marc
AU - Doukhan, Paul
AU - Lang, Gabriel
AU - Ragache, Nicolas
TI - Dependent Lindeberg central limit theorem and some applications
JO - ESAIM: Probability and Statistics
DA - 2008/1//
PB - EDP Sciences
VL - 12
SP - 154
EP - 172
AB - 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(∞), bilinear, Volterra processes, ..., enter this frame.
LA - eng
KW - Central limit theorem; Lindeberg method; weak dependence; kernel density estimation; subsampling; central limit theorem
UR - http://eudml.org/doc/250399
ER -

## References

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