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. © EDP Sciences, SMAI, 2010.