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.
Keywords: central limit theorem, Lindeberg method, weak dependence, kernel density estimation, subsampling
Bardet, Jean-Marc ; Doukhan, Paul 1 ; Lang, Gabriel 2 ; Ragache, Nicolas
@article{PS_2008__12__154_0,
author = {Bardet, Jean-Marc and Doukhan, Paul and Lang, Gabriel and Ragache, Nicolas},
title = {Dependent {Lindeberg} central limit theorem and some applications},
journal = {ESAIM: Probability and Statistics},
pages = {154--172},
year = {2008},
publisher = {EDP-Sciences},
volume = {12},
doi = {10.1051/ps:2007053},
mrnumber = {2374636},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007053/}
}
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 PY - 2008 SP - 154 EP - 172 VL - 12 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2007053/ DO - 10.1051/ps:2007053 LA - en ID - PS_2008__12__154_0 ER -
%0 Journal Article %A Bardet, Jean-Marc %A Doukhan, Paul %A Lang, Gabriel %A Ragache, Nicolas %T Dependent Lindeberg central limit theorem and some applications %J ESAIM: Probability and Statistics %D 2008 %P 154-172 %V 12 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2007053/ %R 10.1051/ps:2007053 %G en %F PS_2008__12__154_0
Bardet, Jean-Marc; Doukhan, Paul; Lang, Gabriel; Ragache, Nicolas. Dependent Lindeberg central limit theorem and some applications. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 154-172. doi: 10.1051/ps:2007053
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