A central limit theorem for triangular arrays of weakly dependent random variables

by    M. H. Neumann

Preprint series: 10-08, Reports on Stochastics and Statistics

M. H. Neumann

60F05 Central limit and other weak theorems
62F40 Bootstrap, jackknife and other resampling methods
62G07 Density estimation
62M15 Spectral analysis

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.

Upload: 2010-08-12

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