Issue |
ESAIM: PS
Volume 14, 2010
|
|
---|---|---|
Page(s) | 299 - 314 | |
DOI | https://doi.org/10.1051/ps:2008030 | |
Published online | 29 October 2010 |
Central limit theorem for sampled sums of dependent random variables
1
Université Claude Bernard – Lyon I, Institut Camille Jordan, Bâtiment Braconnier, 43 avenue du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
2
INSA Toulouse, Institut Mathématique de Toulouse, Équipe de Statistique et Probabilités, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France
Corresponding authors: Corresponding authors: nadine.guillotin@univ-lyon1.fr, Clementine.Prieur@insa-toulouse.fr
Received:
12
December
2007
Revised:
3
June
2008
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
-valued transient random walk. This extends the results
obtained by [N. Guillotin-Plantard and D. Schneider, Stoch. Dynamics 3 (2003) 477–497]. An application
to parametric estimation by random sampling is also provided.
Mathematics Subject Classification: Primary 60F05 / 60G50 / 62D05; Secondary 37C30 / 37E05
Key words: Random walks / weak dependence / central limit theorem / dynamical systems / random sampling / parametric estimation
© EDP Sciences, SMAI, 2010
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