# Dependent Lindeberg central limit theorem and some applications

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

ESAIM: Probability and Statistics (2008)

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

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topBardet, 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 -

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## Citations in EuDML Documents

top- Gabriel Lang, Eric Marcon, Testing randomness of spatial point patterns with the Ripley statistic
- Michael H. Neumann, A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics
- Nadine Guillotin-Plantard, Clémentine Prieur, Central limit theorem for sampled sums of dependent random variables

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