Volume 14, 2010
|Page(s)||299 - 314|
|Published online||29 October 2010|
Central limit theorem for sampled sums of dependent random variables
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
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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