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

Friedrich-Schiller-Universität Jena, Institut für Stochastik, Ernst-Abbe-Platz 2, 07743 Jena, Germany
michael.neumann@uni-jena.de

Received: 18 May 2010

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.