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Central limit theorem for sampled sums of dependent random variables

Published online by Cambridge University Press:  29 October 2010

Nadine Guillotin-Plantard  and
Clémentine Prieur
Nadine Guillotin-Plantard*
Affiliation:
Université Claude Bernard – Lyon I, Institut Camille Jordan, Bâtiment Braconnier, 43 avenue du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
Clémentine Prieur*
Affiliation:
INSA Toulouse, Institut Mathématique de Toulouse, Équipe de Statistique et Probabilités, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France
*
Corresponding authors: nadine.guillotin@univ-lyon1.fr, Clementine.Prieur@insa-toulouse.fr
Corresponding authors: nadine.guillotin@univ-lyon1.fr, Clementine.Prieur@insa-toulouse.fr
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Abstract

We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a ${\mathbb Z}$-valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, Stoch. Dynamics3 (2003) 477–497]. An application to parametric estimation by random sampling is also provided.

Keywords

Random walksweak dependencecentral limit theoremdynamical systemsrandom samplingparametric estimation
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 14 , 2010 , pp. 299 - 314
Copyright
© EDP Sciences, SMAI, 2010

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