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

Michael H. Neumann

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 120-134
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Neumann, Michael H.. "A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics." ESAIM: Probability and Statistics 17 (2013): 120-134. <http://eudml.org/doc/274351>.

@article{Neumann2013,
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.},
author = {Neumann, Michael H.},
journal = {ESAIM: Probability and Statistics},
keywords = {central limit theorem; Lindeberg method; weak dependence; bootstrap; triangular array},
language = {eng},
pages = {120-134},
publisher = {EDP-Sciences},
title = {A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics},
url = {http://eudml.org/doc/274351},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Neumann, Michael H.
TI - A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 120
EP - 134
AB - 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.
LA - eng
KW - central limit theorem; Lindeberg method; weak dependence; bootstrap; triangular array
UR - http://eudml.org/doc/274351
ER -

References

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