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

Published online by Cambridge University Press:  08 February 2013

Michael H. Neumann
Michael H. Neumann*
Affiliation:
Friedrich-Schiller-Universität Jena, Institut für Stochastik, Ernst-Abbe-Platz 2, 07743 Jena, Germany. michael.neumann@uni-jena.de
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Abstract

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 theoremLindeberg methodweak dependencebootstrap.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 120 - 134
Copyright
© EDP Sciences, SMAI, 2013

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