Central limit theorem for sampled sums of dependent random variables

TL;DR

This paper establishes a central limit theorem for sums of dependent random variables under weak dependence, with applications to random sampling and parametric estimation, extending previous results in the field.

Contribution

It introduces a CLT for dependent variables in triangular arrays under weak dependence, extending prior work and applying it to random walk sampling and estimation.

Findings

Proves a CLT for dependent variables with weak dependence conditions.

Applies the theorem to random walk sampling scenarios.

Provides an application to parametric estimation using random sampling.

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 $\bbZ$-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.