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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 Cet article a éte moissonné depuis la source Numdam

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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.

DOI : 10.1051/ps/2011144
Classification : 60F05, 62F40, 62G07, 62M15
Keywords: central limit theorem, Lindeberg method, weak dependence, bootstrap 
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     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 = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011144/}
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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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