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 the study of dependent random variables sampled by a $\mathbb{Z}$-valued transient random walk. This extends the results obtained by Guillotin-Plantard & Schneider (2003). An application to parametric estimation by random sampling is also provided.

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