We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [Stoch. Proc. Appl. 84 (1999) 313-342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics of different type.
Keywords: central limit theorem, Lindeberg method, weak dependence, bootstrap
@article{PS_2013__17__120_0,
author = {Neumann, Michael H.},
title = {A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics},
journal = {ESAIM: Probability and Statistics},
pages = {120--134},
year = {2013},
publisher = {EDP Sciences},
volume = {17},
doi = {10.1051/ps/2011144},
mrnumber = {3021312},
zbl = {1291.60047},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2011144/}
}
TY - JOUR AU - Neumann, Michael H. TI - A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics JO - ESAIM: Probability and Statistics PY - 2013 SP - 120 EP - 134 VL - 17 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2011144/ DO - 10.1051/ps/2011144 LA - en ID - PS_2013__17__120_0 ER -
%0 Journal Article %A Neumann, Michael H. %T A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics %J ESAIM: Probability and Statistics %D 2013 %P 120-134 %V 17 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2011144/ %R 10.1051/ps/2011144 %G en %F PS_2013__17__120_0
Neumann, Michael H. A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 120-134. doi: 10.1051/ps/2011144
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