Central limit theorem for sampled sums of dependent random variables

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. Dynamics 3 (2003) 477-497]. An application to parametric estimation by random sampling is also provided.
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Nadine Guillotin-Plantard, Clémentine Prieur. Central limit theorem for sampled sums of dependent random variables. ESAIM: Probability and Statistics, EDP Sciences, 2010, 14, pp.299-314. ⟨10.1051/ps:2008030⟩. ⟨hal-00200784⟩

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