Central limit theorem for sampled sums of dependent random variables

2007/12/21 by Nadine Guillotin-Plantard, Guillotin-Plantard, Nadine, Clémentine Prieur +1
Mathematics · #37E05 #60G50 #62D05 #FOS: Mathematics #Primary 60F05 #Probability (math.PR) #Secondary 37C30 #math.PR #msc:37C30 #msc:37E05 #msc:60F05 #msc:60G50 #msc:62D05

paper · pdf · doi:10.48550/arxiv.0712.3696

arxiv created 2007/12/21 · arxiv updated 2009/12/01

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.

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