Central limit theorem for sampled sums of dependent random variables
ESAIM: Probability and Statistics, Volume 14  (2010), p. 299-314

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, Stoch. Dynamics 3 (2003) 477-497]. An application to parametric estimation by random sampling is also provided.

DOI : https://doi.org/10.1051/ps:2008030
Classification:  Primary 60F05,  60G50,  62D05,  Secondary 37C30,  37E05
Keywords: random walks, weak dependence, central limit theorem, dynamical systems, random sampling, parametric estimation
@article{PS_2010__14__299_0,
     author = {Guillotin-Plantard, Nadine and Prieur, Cl\'ementine},
     title = {Central limit theorem for sampled sums of dependent random variables},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {14},
     year = {2010},
     pages = {299-314},
     doi = {10.1051/ps:2008030},
     zbl = {pre05872998},
     mrnumber = {2779486},
     language = {en},
     url = {http://www.numdam.org/item/PS_2010__14__299_0}
}
Guillotin-Plantard, Nadine; Prieur, Clémentine. Central limit theorem for sampled sums of dependent random variables. ESAIM: Probability and Statistics, Volume 14 (2010) , pp. 299-314. doi : 10.1051/ps:2008030. http://www.numdam.org/item/PS_2010__14__299_0/

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