by M. H. Neumann
Preprint series: 10-08, Reports on Stochastics and Statistics
M. H. Neumann
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 (1999). The proof uses an apparently new variant of the Lindeberg method where 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 the formulation of our central limit theorem is actually tailor-made for statistics of different type.
Keywords: Central limit theorem, Lindeberg method, weak dependence, bootstrap.