Volume 17, 2013
|Page(s)||120 - 134|
|Published online||08 February 2013|
A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics
Friedrich-Schiller-Universität Jena, Institut für
Received: 18 May 2010
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.
Mathematics Subject Classification: 60F05 / 62F40 / 62G07 / 62M15
Key words: Central limit theorem / Lindeberg method / weak dependence / bootstrap.
© EDP Sciences, SMAI, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.