Central limit theorem for sampled sums of dependent random variables

Nadine Guillotin-Plantard (1) , Clémentine Prieur (2)

1 ICJ - Institut Camille Jordan
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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, (2003) 477-497]. An application to parametric estimation by random sampling is also provided.

Mots clés: Random walks; weak dependence; central limit theorem; dynamical systems; random sampling; parametric estimation

Domaines: Statistiques [math.ST]

Nadine Guillotin-Plantard, Clémentine Prieur. Central limit theorem for sampled sums of dependent random variables. ESAIM: Probability and Statistics, 2010, 14, pp.299-314. ⟨10.1051/ps:2008030⟩. ⟨hal-00200784v1⟩