A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics

Neumann, Michael H.

doi:10.1051/ps/2011144

Neumann, Michael H.

ESAIM: Probability and Statistics, Tome 17 (2013), pp. 120-134.

Résumé

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.

MR Zbl

DOI : 10.1051/ps/2011144

Classification : 60F05, 62F40, 62G07, 62M15
Mots-clés : central limit theorem, Lindeberg method, weak dependence, bootstrap

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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. https://www.numdam.org/articles/10.1051/ps/2011144/

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